Introduction To Corporate Finance Questions and Solutions

INTRODUCTION TO CORPORATE FINANCE 1. Who owns a corporation? Describe the process whereby the owners control the firm’s management. What is the main reason that an agency relationship exists in the corporate form of organization? In this context, what kinds of problems can arise? Answer: In the corporate form of ownership, the shareholders are the owners of the firm. The shareholders elect the directors of the corporation, who in turn appoint the firm’s management. This separation of ownership from control in the corporate form of organization is what causes agency problems to exist. Management may act in its own or someone else’s best interests, rather than those of the shareholders. If such events occur, they may contradict the goal of maximizing the share price of the equity of the firm. 2. Suppose you were the financial manager of a not-for-profit business (a not-for-profit hospital, perhaps). What kinds of goals do you think would be appropriate? Answer: Such organizations frequently pursue social or political missions, so many different goals are conceivable. One goal that is often cited is revenue minimization; i.e., provide whatever goods and services are offered at the lowest possible cost to society. A better approach might be to observe that even a not-for-profit business has equity. Thus, one answer is that the appropriate goal is to maximize the value of the equity. 3. Would the goal of maximizing the value of the stock differ for financial management in a foreign country? Why or why not? Answer: The goal will be the same, but the best course of action toward that goal may be different because of differing social, political, and economic institutions. 4. Suppose you own stock in a company. The current price per share is $25. Another company has just announced that it wants to buy your company and will pay $35 per share to acquire all the outstanding stock. Your company’s management immediately begins fighting off this hostile bid. Is management acting in the shareholders’ best interest? Why or why not? Answer: The goal of management should be to maximize the share price for the current shareholders. If management believes that it can improve the profitability of the firm so that the share price will exceed $35, then they should fight the offer from the outside company. If management believes that this bidder or other unidentified bidders will actually pay more than $35 per share to acquire the company, then they should still fight the offer. However, if the current management cannot increase the value of the firm beyond the bid price, and no other higher bids come in, then management is not acting in the interests of the shareholders by fighting the offer. Since current managers often lose their jobs when the corporation is acquired, poorly monitored managers have an incentive to fight corporate takeovers in situations such as this. 5. Why is the goal of financial management to maximize the current share price of the company’s stock? In other words, why isn’t the goal to maximize the future share price? Answer: Maximizing the current share price is the same as maximizing the future share price at any future period. The value of a share of stock depends on all of the future cash flows of company. Another way to look at this is that, barring large cash payments to shareholders, the expected price of the stock must be higher in the future than it is today. Who would buy a stock for $100 today when the share price in one year is expected to be $80? DISCOUNTED CASH FLOW VALUATION 1. As you increase the length of time involved, what happens to future values? What happens to present values? Answer: Assuming positive cash flows and interest rates, the future value increases and the present value decreases. 2. What happens to the future value of an annuity if you increase the rate r? What happens to the present value? Answer: Assuming positive cash flows and interest rates, the present value will fall and the future value will rise. 3. On subsidized Stafford loans, a common source of financial aid for college students, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman or a senior? Explain. Answer: A freshman does. The reason is that the freshman gets to use the money for much longer before interest starts to accrue. 4. Compute the future value of $1,000 compounded annually for a. 10 years at 5 percent b. 10 years at 10 percent c. 20 years at 5 percent d. Why is the interest earned in part © not twice the amount earned in part (a)? Solution: To find the FV of a lump sum, we use: FV = PV(1 + r)t a. 0 10 $1,000 FV FV = $1,000(1.05)10 = $1,628.89 b. 0 10 $1,000 FV FV = $1,000(1.10)10 = $2,593.74 c. 0 20 $1,000 FV FV = $1,000(1.05)20 d. 5. = $2,653.30 Because interest compounds on the interest already earned, the interest earned in part c is more than twice the interest earned in part a. With compound interest, future values grow exponentially. For each of the following, compute the present value: Present Value Years 6 9 18 23 Interest Rate 7% 15 11 18 Future Value $13,827 43,852 725,380 590,710 Solution: To find the PV of a lump sum, we use: PV = FV / (1 + r)t 0 6 PV $13,827 PV = $13,827 / (1.07)6 = $9,213.51 0 9 PV $43,852 PV = $43,852 / (1.15)9 = $12,465.48 0 18 PV $725,380 PV = $725,380 / (1.11)18 = $110,854.15 0 23 PV $590,710 PV = $590,710 / (1.18)23 6. = $13,124.66 Solve for the unknown interest rate in each of the following: Present Value $242 410 51,700 18,750 Years 4 8 16 27 Interest Rate Future Value $307 896 162,181 483,500 Solution: To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1 / t – 1 0 4 –$242 $307 FV = $307 = $242(1 + r)4; r = ($307 / $242)1/4 – 1 = 6.13% 0 8 –$410 $896 FV = $896 = $410(1 + r)8; r = ($896 / $410)1/8 – 1 = 10.27% 0 16 $162,181 –$51,700 FV = $162,181 = $51,700(1 + r)16; r = ($162,181 / $51,700)1/16 – 1 = 7.41% 0 27 $483,500 –$18,750 FV = $483,500 = $18,750(1 + r)27; 7. r = ($483,500 / $18,750)1/27 – 1 = 12.79% At 8 percent interest rate, how long does it take to double your money? To quadruple it? Solution: To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) The length of time to double your money is: 0 ? –$1 $2 FV = $2 = $1(1.08)t t = ln 2 / ln 1.08 = 9.01 years The length of time to quadruple your money is: 0 ? –$1 $4 FV = $4 = $1(1.08)t t = ln 4 / ln 1.08 = 18.01 years Notice that the length of time to quadruple your money is twice as long as the time needed to double your money (the difference in these answers is due to rounding). This is an important concept of time value of money. 8. An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $150 annually if the next payment occurs one year from today? The market interest rate is 4.6%. Solution: The time line is: 0 ∞ 1 … PV $150 $150 $150 $150 $150 $150 $150 $150 $150 A consol is a perpetuity.To find the PV of a perpetuity, we use the equation: PV = C / r PV = $150 / .046 PV = $3,260.87 9. An investment offers $4,900 per year for 15 years, with the first payment occurring one year from now. If the required return is 8%, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever? Solution: To find the PVA, we use the equation: PVA = C({1 – [1/(1 + r)]t } / r ) 0 PV 1 $4,900 PVA@15 yrs: 0 15 $4,900 $4,900 $4,900 … $4,900 $4,900 $4,900 $4,900 $4,900 PVA = $4,900{[1 – (1/1.08)15 ] / .08} = $41,941.45 1 40 … PV $4,900 PVA@40 yrs: $4,900 $4,900 $4,900 $4,900 $4,900 PVA = $4,900{[1 – (1/1.08)40 ] / .08} = $58,430.61 $4,900 $4,900 $4,900 0 PV 1 $4,900 PVA@75 yrs: 75 $4,900 $4,900 $4,900 … $4,900 $4,900 $4,900 $4,900 $4,900 PVA = $4,900{[1 – (1/1.08)75 ] / .08} = $61,059.31 To find the PV of a perpetuity, we use the equation: PV = C / r 0 PV 1 $4,900 ∞ $4,900 $4,900 $4,900 … $4,900 $4,900 $4,900 $4,900 $4,900 PV = $4,900 / .08 PV = $61,250 Notice that as the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. The present value of the 75-year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only $190.69. NET PRESENT VALUE AND OTHER INVESTMENT RULES 1. If a project with conventional cash flows has a payback period less than the project’s life, can you definitively state the algebraic sign of NPV? Why or why not? If you know the discounted payback period is less than the project’s life, what can you say about the NPV? Explain. Answer: Assuming conventional cash flows, a payback period less than the project’s life means that the NPV is positive for a zero discount rate, but nothing more definitive can be said. For discount rates greater than zero, the payback period will still be less than the project’s life, but the NPV may be positive, zero, or negative, depending on whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback includes the effect of the relevant discount rate. If a project’s discounted payback period is less than the project’s life, it must be the case that NPV is positive. 2. Suppose a project has conventional cash flows and a positive NPV. What do you know about its payback? Its discounted payback? Its profitability index? Its IRR? Explain. Answer: Assuming conventional cash flows, if a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a zero discount rate; thus, the payback period must be less than the project life. Since discounted payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback period must be less than the project’s life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost; thus, PI must be greater than 1. If NPV is positive for a certain discount rate R, then it will be zero for some larger discount rate R*; thus, the IRR must be greater than the required return. 3. Define each of the following investment rules and discuss any potential shortcomings of each. In your definition, state the criterion for accepting or rejecting independent projects under each rule. a. Payback period b. Internal rate of return c. Profitability index d. Net present value Answer: a. Payback period is simply the accounting break-even point of a series of cash flows. To actually compute the payback period, it is assumed that any cash flow occurring during a given period is realized continuously throughout the period, and not at a single point in time. The payback is then the point in time for the series of cash flows when the initial cash outlays are fully recovered. Given some predetermined cutoff for the payback period, the decision rule is to accept projects that pay back before this cutoff, and reject projects that take longer to pay back. The worst problem associated with the payback period is that it ignores the time value of money. In addition, the selection of a hurdle point for the payback period is an arbitrary exercise that lacks any steadfast rule or method. The payback period is biased towards shortterm projects; it fully ignores any cash flows that occur after the cutoff point. b. The IRR is the discount rate that causes the NPV of a series of cash flows to be identically zero. IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate, the net value of the project is zero. The acceptance and rejection criteria are: If C0< 0 and all future cash flows are positive, accept the project if the internal rate of return is greater than or equal to the discount rate. If C0< 0 and all future cash flows are positive, reject the project if the internal rate of return is less than the discount rate. If C0> 0 and all future cash flows are negative, accept the project if the internal rate of return is less than or equal to the discount rate. If C0> 0 and all future cash flows are negative, reject the project if the internal rate of return is greater than the discount rate. IRR is the discount rate that causes NPV for a series of cash flows to be zero. NPV is preferred in all situations to IRR; IRR can lead to ambiguous results if there are non-conventional cash flows, and it also may ambiguously rank some mutually exclusive projects. However, for stand-alone projects with conventional cash flows, IRR and NPV are interchangeable techniques. 4. c. The profitability index is the present value of cash inflows relative to the project cost. As such, it is a benefit/cost ratio, providing a measure of the relative profitability of a project. The profitability index decision rule is to accept projects with a PI greater than one, and to reject projects with a PI less than one. The profitability index can be expressed as: PI = (NPV + cost)/cost = 1 + (NPV/cost). If a firm has a basket of positive NPV projects and is subject to capital rationing, PI may provide a good ranking measure of the projects, indicating the “bang for the buck” of each particular project. d. NPV is simply the present value of a project’s cash flows, including the initial outlay. NPV specifically measures, after considering the time value of money, the net increase or decrease in firm wealth due to the project. The decision rule is to accept projects that have a positive NPV, and reject projects with a negative NPV. NPV is superior to the other methods of analysis presented in the text because it has no serious flaws. The method unambiguously ranks mutually exclusive projects, and it can differentiate between projects of different scale and time horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and thus not certain, but this is a problem shared by the other performance criteria as well. A project with NPV = $2,500 implies that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted. Fuji Software, Inc., has the following mutually exclusive projects. Year 0 1 2 3 Project A -$15,000 9,500 6,000 2,400 Project B -$18,000 10,500 7,000 6,000 a. Suppose Fuji’s payback period cutoff is two years. Which of these two projects should be chosen? b. Suppose Fuji uses the NPV rule to rank these two projects. Which project should be chosen if the appropriate discount rate is 15 percent? Solution: a. The payback period is the time that it takes for the cumulative undiscounted cash inflows to equal the initial investment. Project A: Cumulative cash flows Year 1 = $9,500 Cumulative cash flows Year 2 = $9,500 + 6,000 = $9,500 = $15,500 Companies can calculate a more precise value using fractional years. To calculate the fractional payback period, find the fraction of year 2’s cash flows that is needed for the company to have cumulative undiscounted cash flows of $15,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 1 by the undiscounted cash flow of year 2. Payback period = 1 + ($15,000 – 9,500) / $6,000 Payback period = 1.917 years Project B: Cumulative cash flows Year 1 = $10,500 Cumulative cash flows Year 2 = $10,500 + 7,000 Cumulative cash flows Year 3 = $10,500 + 7,000 + 6,000 = $10,500 = $17,500 = $23,500 To calculate the fractional payback period, find the fraction of year 3’s cash flows that is needed for the company to have cumulative undiscounted cash flows of $18,000. Divide the difference between the initial investment and the cumulative undiscounted cash flows as of year 2 by the undiscounted cash flow of year 3. Payback period = 2 + ($18,000 – 10,500 – 7,000) / $6,000 Payback period = 2.083 years Since project A has a shorter payback period than project B has, the company should choose project A. b. Discount each project’s cash flows at 15 percent. Choose the project with the highest NPV. Project A: NPV = –$15,000 + $9,500 / 1.15 + $6,000 / 1.152 + $2,400 / 1.153 NPV = –$624.23 Project B: NPV = –$18,000 + $10,500 / 1.15 + $7,000 / 1.152 + $6,000 / 1.153 NPV = $368.54 The firm should choose Project B since it has a higher NPV than Project A has. 5. An investment project has annual cash inflows of $5,000, $5,500, $6,000, and $7,000, and a discount rate of 14 percent. What is the discounted payback period for these cash flows if the initial cost is $8,000? What if the initial cost is $12,000? What if it is $16,000? Solution: When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = $5,000/1.14 = $4,385.96 Value today of Year 2 cash flow = $5,500/1.142 = $4,232.07 Value today of Year 3 cash flow = $6,000/1.143 = $4,049.83 Value today of Year 4 cash flow = $7,000/1.144 = $4,144.56 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $4,385.96, so the discounted payback for an initial cost of $8,000 is: Discounted payback = 1 + ($8,000 – 4,385.96)/$4,232.07 = 1.85 years For an initial cost of $12,000, the discounted payback is: Discounted payback = 2 + ($12,000 – 4,385.96 – 4,232.07)/$4,049.83 = 2.84 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback. If the initial cost is $16,000, the discounted payback is: Discounted payback = 3 + ($16,000 – 4,385.96 – 4,232.07 – 4,049.83) / $4,144.56 = 3.80 years 6. Stone Sour, Inc., has a project with the following cash flows: Year 0 1 2 3 Cash Flows ($) -$20,000 8,500 10,200 6,200 The company evaluates all projects by applying the IRR rule. If the appropriate interest rate is 9 percent, should the company accept the project? Solution: The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3 0 = –$20,000 + $8,500/(1 + IRR) + $10,200/(1 + IRR)2 + $6,200/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 12.41% Since the IRR is greater than the required return we would accept the project. 7. Bill plans to open a self-serve grooming center in a storefront. The grooming equipment will cost $385,000, to be paid immediately. Bill expects after-tax cash inflows of $84,000 annually for seven years, after which he plans to scrap the equipment and retire to the beaches of Nevis. The first cash inflow occurs at the end of first year. Assume the required return is 13 percent. What is the project’s PI? Should it be accepted? Solution: The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The cash flows from this project are an annuity, so the equation for the profitability index is: PI = C(PVIFAR,t) / C0 PI = $84,000(PVIFA13%,7) / $385,000 PI = .965