Final Exam a Review of Tough Stuff

Final Exam a Review of Tough Stuff 1. You invest $100 at the beginning of each year for the next 10 years. The interest rate is 10 percent, What is the future value? 100 109 100 2 + + 1 + 3 4 5 6 7 10 *ywcan also use excel to solve thi by entering +PVC-1,10,-100,0, 15 house it is the '1'is an analy ①N=4 1/3 = 10 PV=0 PMT = -100 CPT FV = 1,357,95 = Fu of qur annuity@and of year a @N=1 11:10 PV=-1357.95 PMT=0 CPTFV = 1,493.75= FVol 9ur annuity Cend of year 10 ③N=10 11' * 1 = 10 PV=-100 PMIT=0 CPTFV=359.37=FV of investment @enst of year 10 Future valve 1.493 * 0.75 + 259.37 > 1.753 * 0.12 2. You want to build a house expect to need another $50,000. If he can save 9000 at the end of each year, what rate of return must he earn in order to have the amount needed? 9000 9000 9000 + 9000 1Fv=50,000 0 2 3 4 N = W PV=0 PMT-9000 FV:50, CPT 1/4 = 32.395% rate of return = 22395% 3. Dr. Danielsen is selling a stock for $30,000. He bought it for $16,400 ten years ago. What is the annual return on his investment? PV: -16,400 i = Fu30,000 0 n=10 N=10 PV:-16400 PMT=0 FV=30,000 CPT 1/4 = 6.225% annual return=6.225% 4. You will deposit $1,000 today. It will grow for 4 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 5%. Your annual withdrawal will be: (① PV:1000 i = (10%)/2 = 5% N= x * 4 = 5 Pus-1000 PAT20 CPTFU 1477.46 i = 5% n=4x2=8 ③P=1477.46 A? A? A? + 0 1 A? + N=4 114-5 pv=-1477.46 FV20 CPT PMT-416.66-A 2 3 annual withdrawal= $416.66 PV:100,000 0 5. Mark borrowed $100,000 to buy a house. His loan cost was 5% and he promised to repay the loan in 10 equal annual payments. What is the principal outstanding after the first loan payment? 13950 12A50 + 3 12950 0,960 1950 5 6 7 10 12960 17,450 12,960 12,950 + 4 + + N =10 1WY=5 Pus-100,000 FV=0 CPT PMT = 12,450-46 = annual Payments interest expense in first Payment 100,000.05 = 5,000 12,950.46-5000 7950-46 pencipal repayment $100,000-7950.46=393,049.54 Principal outstandi 6. A 10-year zero-coupon bond that yields 6% is issued with a $1000 par value. What are the coupon payments? Zero! What is the issuance price of the bond (round to the nearest dollar)? Issuance Price Pu N=10 11Y-6 PMT=0 FV=-1000 CPT PV=3358.39 issuance price = $558.39 7. The risk premium is likely to be highest for stocks bonds U.S. treasuries Stocks! *The risk Premium is the expected return in excess of the risk-free rate 8. A 10-year bond pays 10% on a face value of $1,000. If similar bonds are currently yielding 5%, what is the market value of the bond? Use annual analysis. 4 + 100 180 100 100 + + + + 100 100 100 LSD 100 0 1 3 5 6 7 10 N-10 114=5 PMT -100 FV=-1000 CPT PV= 1386.09 market value = $1,386.09 * the market value is the Puof future cash flows 9. An issue of common stock's most recent dividend is $2. Its growth rate is 6%. What is its price if the market's rate of return is 9%? D_{0} = 2 D_{1} = 2(1 + g) = 2.12 = 2(1.06) Price: $70.67 P = D_{1}/(6 - g) = 2.12 .09..06 = 2.12 .03 =5.10.67 10. A 20-year bond pays $100 in interest each year and has a face value of $1,000. If similar bonds are currently yielding 5%, what is the market value of the bond? Use annual analysis 100 100 55 10 100 + 10 FV=1000 0 18 19 FV=-1000 CPT PV=1,623.11 N = 20 1 / Y = 5 PMT=-100 market value = $1,623.11 11. Acme Co. has an optimal capital structure that is 60% common equity, 30% debt, and 10% preferred stock. Acme's pretax cost of equity is 10%. Its pretax cost of preferred equity is 8%, and its pretax cost of debt is also 6%. If the corporate tax rate is 50%, what is the weighed average cost of capital? K_{e} = 10% * 60% = 0.06 K_{p} = 8% pi * 10% = 0.008 K_{d} = 6% * (1 - 0.5) = 3% * 30% = 0.009/0.077 *notice that only Vid is impacted by the tax rate. Taxes don't impact he or h_{P} WACC: 7.7% مرة Po 12. Using the constant growth model, a firm's expected (D) dividend yield of the stock price, is 2% and its growth rate is 7%. If the tax rate is .35%, what is the firm's cost of equity? Po he=+9 요 NIA-it's equity! Don't be fooled! he=.02+.07.09 Cost of equity: 9% 13. Which projects should be accepted relative to the WACC? accept Projects when IRR > WACC 14. A project requires an investment of $1000 and has a net present value of $500. If the IRR is 5%, what is the profitability index for the project? Profitability index= Npus inflows-outflows! 500-inflous-1000 inflows: 1500 Pv inflows 1500 PV out flous 1000 Pu inflows: 1500 ( = 1.5 Proutflows: 1000 Profitability index = 1.5 15. Why is NPV a better method of evaluating projects than IRR? look it up! 16. Firm X is considering the replacement of an old machine that can be sold for $10,000 but has a book value is $5,000. The firm's tax rate for ordinary income is 20%. What is the net cash flow from the sale of the old machine? Accounting Cash flows Proceeds 10,000 +10,000 *Gams are not cash flows, but taxes are! less bosis -5,000 gain 5,000 raxes -1000 -1,000 9,000 net cash flow 17. 320 Corp. is considering a $100,000 investment that will provide annual cash flows of $25,000 for the next 5 years. The firm has a 10% cost of capital, Should the firm take the project? Use NPV and IRR analysis. nominal yield = 10% -unchanged ( 10 + acc = 10/100 = 10% ) NPV analysis Vinflows: N=5 1 / r = 10 PMT=25,000 FV=0 CPTPV:94,769-66=Puinflaws NPU: Puinflows- Proutflows = 94 ,769.66-100,000 = - 3 ,330.34 negative Pu, donot take Project IRR Analysi's N=5 PV=-100,000 PMT=25,000 FV=0 CPT 1/4=7.43% rate of returm: 7.93% Cost of capital > rate of return 10% 7.93% do not take Project 18. Consider this 2 year bond with a 10% coupon rate and a $100 maturity value. When issued, the following is true: The nominal yield is 10% ($10 coupon payment/$100 face value) The current price is $100 The current yield is 10% ($10 coupon payment/$100 price) The yield to maturity is 10% If interest rates fall to 9%, what are the nominal yield, yield to maturity, new price, and current yield? 10 10 Fv = 100 0 2 the yield to maturity is 9% Price = $101.76 (N=2 11429 PART=-10 Fu=100 CPTPV=101.76) Current yield: 9.83% (10%pu= 1/101.76=.0983) *notice that when YTM fell, the current vield also fell