Introduction To Corporate Finance (Making Capital Investment Decisions)

MAKING CAPITAL INVESTMENT DECISIONS 1. In the context of capital budgeting, what is an opportunity cost? Answer: In this context, an opportunity cost refers to the value of an asset or other input that will be used in a project. The relevant cost is what the asset or input is actually worth today, not, for example, what it cost to acquire. 2. Which of the following should be treated as an incremental cash flow when computing the NPV of an investment? a. A reduction in the sales of a company’s other products caused by the investment. b. An expenditure on the plant and equipment that has not yet been made and will be made only if the project is accepted. c. Costs of research and development undertaken in connection with the product during the past three years. d. Annual depreciation expense from the investment. e. Dividend payments by the firm. f. The resale value of the plant and equipment at the end of the project’s life. g. Salary and medical costs for production personnel who will be employed only if the project is accepted. Answer: a. Yes, the reduction in the sales of the company’s other products, referred to as erosion, should be treated as an incremental cash flow. These lost sales are included because they are a cost (a revenue reduction) that the firm must bear if it chooses to produce the new product. b. Yes, expenditures on plant and equipment should be treated as incremental cash flows. These are costs of the new product line. However, if these expenditures have already occurred (and cannot be recaptured through a sale of the plant and equipment), they are sunk costs and are not included as incremental cash flows. c. No, the research and development costs should not be treated as incremental cash flows. The costs of research and development undertaken on the product during the past three years are sunk costs and should not be included in the evaluation of the project. Decisions made and costs incurred in the past cannot be changed. They should not affect the decision to accept or reject the project. d. Yes, the annual depreciation expense must be taken into account when calculating the cash flows related to a given project. While depreciation is not a cash expense that directly affects cash flow, it decreases a firm’s net income and hence, lowers its tax bill for the year. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation. 3. e. No, dividend payments should not be treated as incremental cash flows. A firm’s decision to pay or not pay dividends is independent of the decision to accept or reject any given investment project. For this reason, dividends are not an incremental cash flow to a given project. Dividend policy is discussed in more detail in later chapters. f. Yes, the resale value of plant and equipment at the end of a project’s life should be treated as an incremental cash flow. The price at which the firm sells the equipment is a cash inflow, and any difference between the book value of the equipment and its sale price will create accounting gains or losses that result in either a tax credit or liability. g. Yes, salary and medical costs for production employees hired for a project should be treated as incremental cash flows. The salaries of all personnel connected to the project must be included as costs of that project. Raphael Restaurant is considering the purchase of a $9,000 souffle maker. The soufflé maker has an economic life of 5 years and will be fully depreciated by the straight-line method. The machine will produce 1,500 souffles per year, with each costing $2.30 to make and priced at $4.75. assume that the discount rate is 14 percent and the tax rate is 34 percent. Should Raphael make the purchase? Solution: Using the tax shield approach to calculating OCF, we get: OCF = (Sales – Costs)(1 – tC) + tCDepreciation OCF = [($4.75 × 1,500) – ($2.30 × 1,500)](1 – 0.34) + 0.34($9,000/5) OCF = $3,037.50 So, the NPV of the project is: NPV = –$9,000 + $3,037.50(PVIFA14%,5) NPV = $1,427.98 4. Down Under Boomerang, Inc., is considering a new 3-year expansion project that requires an initial fixed asset investment of $1.4 million. The fixed asset will be depreciated straight line to zero over its 3-year tax life, after which it will be worthless. The project is estimated to generate $1,120,000 in annual sales, with costs of $480,000. The tax rate is 35 percent and the required return in 12 percent. What is the project’s NPV? Solution: Using the tax shield approach to calculating OCF, we get: OCF = (Sales – Costs)(1 – tC) + tCDepreciation OCF = ($1,120,000 – 480,000)(1 – 0.35) + 0.35($1,400,000/3) OCF = $579,333.33 So, the NPV of the project is: NPV = –$1,400,000 + $579,333.33(PVIFA12%,3) NPV = –$8,539.09 5. In the previous problem, suppose the project requires an initial investment in net working capital of $285,000 and the fixed asset will have a market value of $225,000 at the end of the project. What is the project’s year 0 net cash flow? Year 1? Year 2? Year 3? What is the new NPV? Solution: The cash outflow at the beginning of the project will increase because of the spending on NWC. At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we also must account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be: Year 0 1 2 3 Cash Flow – $1,685,000 579,333.33 579,333.33 1,010,583.33 = –$1,400,000 – 285,000 = $579,333.33 + 285,000 + 225,000 + (0 – 225,000)(.35) And the NPV of the project is: NPV = –$1,685,000 + $579,333.33(PVIFA12%,2) + ($1,010,583.33 / 1.123) NPV = $13,416.15 INTEREST RATES AND BOND VALUATION 1. Which has greater interest rate risk, a 30-year Treasury bond or a 30-year BB corporate bond? Answer: All else the same, the Treasury security will have lower coupons because of its lower default risk, so it will have greater interest rate risk. 2. How does a bond issuer decide on the appropriate coupon rate to set on its bond? Explain the difference between coupon rate and the required return on a bond. Answer: Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used to establish the coupon rate necessary for a particular issue to initially sell for par value. Bond issuers also simply ask potential purchasers what coupon rate would be necessary to attract them. The coupon rate is fixed and simply determines what the bond’s coupon payments will be. The required return is what investors actually demand on the issue, and it will fluctuate through time. The coupon rate and required return are equal only if the bond sells for exactly at par. 3. a. What is the relationship between the price of a bond and its yield to maturity(YTM)? b. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about the discount bonds? For bonds selling at par value? c. What is the relationship between current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value? Answer: a. The bond price is the present value of the cash flows from a bond. The YTM is the interest rate used in valuing the cash flows from a bond. b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate. c. Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all cases, the current yield plus the expected one-period capital gains yield of the bond must be equal to the required return. 4. What is the price of a 15-year, zero coupon bond paying $1,000 at maturity if the YTM is: a. 5 percent? b. 10 percent? c. 15 percent? Solution: The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are no coupon payments, the periods are semiannual to stay consistent with coupon bond payments. So, the price of the bond for each YTM is: a. P = $1,000/(1 + .05/2)30 = $476.74 b. P = $1,000/(1 + .10/2)30 = $231.38 c. P = $1,000/(1 + .15/2)30 = $114.22 5. Microhard has issued a bond with the following characteristics: Par: $1,000 Time to maturity: 15 years Coupon rate: 7% Semiannual payments Calculate the price of this bond if the YTM is: a. 7 percent b. 9 percent c. 5 percent Solution: The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes a semiannual coupon. The price of the bond at each YTM will be: a. P = $35({1 – [1/(1 + .035)]30 } / .035) + $1,000[1 / (1 + .035)30] P = $1,000.00 When the YTM and the coupon rate are equal, the bond will sell at par. b. P = $35({1 – [1/(1 + .045)]30 } / .045) + $1,000[1 / (1 + .045)30] P = $837.11 When the YTM is greater than the coupon rate, the bond will sell at a discount. c. P = $35({1 – [1/(1 + .025)]30 } / .025) + $1,000[1 / (1 + .025)30] P = $1,209.30 When the YTM is less than the coupon rate, the bond will sell at a premium. 6. Waters Umbrella Corp. issued 15-year bonds two years ago at a coupon rate of 6.4 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM? Solution: Here we are finding the YTM of a semiannual coupon bond. The bond price equation is: P = $1,050 = $32(PVIFAR%,26) + $1,000(PVIFR%,26) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 2.923% Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM = 2 7. 2.923% = 5.85% Rhiannon Corporation has bonds on the market with 11.5 years to maturity, a YTM of 7.6 percent, and a current price of $1,060. The bonds make semiannual payments. What must the coupon rate be on these bonds? Solution: Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $1,060 = C(PVIFA3.8%,23) + $1,000(PVIF3.8%,23) Solving for the coupon payment, we get: C = $41.96 Since this is the semiannual payment, the annual coupon payment is: 2 × $41.96 = $83.92 And the coupon rate is the annual coupon payment divided by par value, so: Coupon rate = $83.92 / $1,000 = .0839, or 8.39% 8. A Japanese company has a bond outstanding that sells for 92 percent of its ¥100,000 par value. The bond has a coupon rate of 2.8 percent paid annually and matures in 21 years. What is the yield to maturity of this bond? Solution: Here we are finding the YTM of an annual coupon bond. The fact that the bond is denominated in yen is irrelevant. The bond price equation is: P = ¥92,000 = ¥2,800(PVIFAR%,21) + ¥100,000(PVIFR%,21) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 3.34% Since the coupon payments are annual, this is the yield to maturity. STOCK VALUATION 1. Why does the value of a share of stock depend on dividends? Answer: The value of any investment depends on the present value of its cash flows; i.e., what investors will actually receive. The cash flows from a share of stock are the dividends. 2. A substantial percentage of the companies listed on stock exchanges don’t pay dividends, but investors are nonetheless willing to buy shares in them. How is this possible given your answer to the previous question? Answer: Investors believe the company will eventually start paying dividends (or be sold to another company). 3. Referring to the previous questions, under what circumstances might a company choose not to pay dividends? Answer: In general, companies that need the cash will often forgo dividends since dividends are a cash expense. Young, growing companies with profitable investment opportunities are one example; another example is a company in financial distress. 4. Suppose a company has a preferred stock issue and a common stock issue. Both have just paid $2 dividend. Which do you think will have a higher price, a share of the preferred or a share of the common? Answer: The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the preferred. However, the preferred is less risky because of the dividend and liquidation preference, so it is possible the preferred could be worth more, depending on the circumstances. 5. The Starr Co. just paid a dividend of $2.15 per share on its stock. The dividends are expected to grow at a constant rate of 5 percent per year, indefinitely. If investors require a return of 11 percent on the stock, what is the current price? What will the price be in three years? In 15 years? Solution: The constant dividend growth model is: P t = Dt × (1 + g) / (R – g) So, the price of the stock today is: P 0 = D0(1 + g) / (R – g) = $1.90 (1.05) / (.11 – .05) = $37.63 The dividend at year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so: P 3 = D3(1 + g) / (R – g) = D0(1 + g)4/ (R – g) = $1.90 (1.05)4/ (.11 – .05) = $43.56 We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: P 15 = D15(1 + g) / (R – g) = D0(1 + g)16/ (R – g) = $1.90 (1.05)16/ (.11 – .05) = $78.22 There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be: P 3 = P0(1 + g)3 = $37.63(1 + .05)3 = $43.56 And the stock price in 15 years will be: P 15 = P0(1 + g)15 = $37.63(1 + .05)15 = $78.22 6. The next dividend payment by ECY, Inc., will be $3.20 per share. The dividends are anticipated to maintain a growth rate of 6 percent, forever. If ECY stock currently sells for $63.50 per share, what is the required return? Solution: We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find: R = (D1 / P0) + g = ($3.20 / $63.50) + .06 = .1104, or 11.04% 7. For the company in the previous problem, what is the dividend yield? What is the expected capital gains yield? Solution: The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1 / P0 = $3.20 / $63.50 = .0504, or 5.04% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 6% 8. White Wedding Corporation will pay a $2.65 per share dividend next year. The company pledges to increase its dividend by 4.75 percent per year, indefinitely. If you require a return of 11 percent on your investment, how much will you pay for the company’s stock today? Solution: Using the constant growth model, we find the price of the stock today is: P 0 = D1 / (R – g) = $2.65 / (.11 – .0475) = $42.40 9. Ayden, Inc., has an issue of preferred stock outstanding that pays a $5.90 dividend every year, in perpetuity. If this issue currently sells for $87 per share, what is the required return? Solution: The price of a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember that most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is: R = D/P0 = $5.90/$87 = .0678, or 6.78%