FOR CORPORATE FINANCE
1. If someone promises to pay $1,000 each year in perpetuity, what is that promise worth if discount rate is 16%? (A: $6,250)
2. PRESENT VALUE ANNUITY:
You are going to withdraw $5,000 at the end of each year for the next four years from an account that pays interest at a rate of 9% compounded annually. How much must there be in the account today in order for the account to reduce to a balance of zero after the last withdrawal?
(Response: PVA = $5,000 {[1 - (1 / 1.094)] / .09} = $16,198.60)
3. PRESENT VALUE ANNUITY:
At the end of each year for the next 8 years you will receive cash flows of $500. If the appropriate discount rate is 7.5%, how much would you pay for this annuity?
(Response: PVA = $500 {[1 - (1 / 1.0758)] / .075} = $2,928.65)
4. PRESENT VALUE ANNUITY DUE:
In order to help you through college, your parents just deposited $20,000 into a bank account paying 6% interest. Starting tomorrow, you plan to withdraw equal amounts from the account at the beginning of each of the next four years. What is the MOST you can withdraw annually?
(Response: PVAdue = $20,000 = C {[1 - (1 / 1.064)] / .06} (1.06); C = $5,445.12)
5. FUTURE VALUE ANNUITY DUE:
What is the future value in 12 years of $800 payments received at the beginning of each year for the next 12 years? Assume an interest rate of 8.25%.
(Response: FVAdue = $800 [(1.082512 -1) / .0825] (1.0825) = $16,679.86)
6. Dizzy Corporation bonds bearing a coupon rate of 12%, pay coupons semiannually, have 3 years remaining to maturity, and are currently priced at $940 per bond. What is the yield to maturity?
(Response: $940 = $60{[1 - 1/(1 + R)6] / R} + 1,000 / (1 + R)6; R = 7.27%; YTM = 7.27% x 2 = 14.54%)
7. J&J Manufacturing just issued a bond with a $1,000 face value and a coupon rate of 8%. If the bond has a life of 20 years, pays annual coupons, and the yield to maturity is 7.5%, what will the bond sell for?
(Response: price = $80 [(1 - 1/1.07520) / .075] + 1,000 / 1.07520 = $1,050.97)
8. What would you pay for a bond that pays an annual coupon of $45, has a face value of $1,000, matures in 11 years, and has a yield to maturity of 10%?
(Response: price = $45 [(1 - 1/1.111) / .1] + 1,000 / 1.111 = $642.77)
9. King Noodles' bonds have a 9% coupon rate. Interest is paid quarterly and the bonds have a maturity of 10 years. If the appropriate discount rate is 10% on similar bonds, what is the price of King Noodles' bonds?
(Response: price = $22.50 [(1 - 1/1.02540) / .025] + 1,000 / 1.02540 = $937.24)
10. What would you pay for a share of ABC Corporation stock today if the next dividend will be $3 per share, your required return on equity investments is 15%, and the stock is expected to be worth $90 one year from now?
(Response: P0 = $3 / 1.15 + 90 / 1.15 = $80.87)
11. The dividend on Simple Motors common stock will be $3 in 1 year, $4.25 in 2 years, and $6.00 in 3 years. You can sell the stock for $100 in 3 years. If you require a 12% return on your investment, how much would you be willing to pay for a share of this stock today?
(Response: P0 = $3.00 / 1.12 + 4.25 / 1.122 + 106 / 1.123 = $81.52)
12. IBM Ltd paid a dividend of $4 at the end of the year. It is expected to grow by 8% each year for the next 4 years. The market price of the shares is expected to be $60 at the end of 4 years. Assuming 12% required rate of return of investors, at what price should the shares of IBM Ltd sell? ($52.75)
13. An investor has invested in the shares of IBM Ltd, which expects no growth in dividends. IBM Ltd has paid a dividend of $3 per share. If the required rate of return is 14%, what would be the value of the share? ($21.43)
14. The required rate of return of investors is 15%. IBM Ltd declared and paid annual dividend of $4 per share. It is expected to grow 20% for the next 2 years and at 10% thereafter. Compute the price at which the shares should sell? ($104.42)
15. IBM is considering two investments both of which cost $10,000. The cash flows are as follows:
Year Project A Project B
1 6,000 5,000
2 4,000 3,000
3 3,000 8,000
Which of the two projects should be chosen based on the payback method?
(A: project A is the best)
Which of the two projects should be chosen based on the net present value method? Assuming a cost of capital of 10% (A: project B is the best)
16. Suppose that the net earning for the next 4 years is estimated to be $10,000, $15,000, $20,000, and $30,000, respectively. If the initial investment is $100,000 (If preset limit is 30%)
Required: Calculate the average rate of return and the project is accepted or rejected? (A: 38%)
17. NET PRESENT VALUE:
Would you accept a project which is expected to pay $2,500 a year for 6 years if the initial investment is $10,000 and your required return is 8%?
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