# Time Value of Money

1) Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a ?xed retirement income that has the same purchasing power at the time he retires as \$40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. In?ation is expected to be 5 percent per year from today forward; he currently has \$100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding.

To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal? (Show the time line)2) A father is planning a savings program to put his daughter through college. His daughter is now 13 and the daughter plans to enroll at the university in 5 years. She would take 4 years to complete her graduation. Currently, the cost of education is \$12,500 per year, but a 5 percent annual inflation rate in these cost is forecasted. The daughter recently inherited \$7,500 from her grandfather, which the father plans to invest in a bank paying 8 percent interest compound annually, to help meet the cost of the daughter’s education. However, the remaining cost will be met by money, the father will deposit in the savings account. He will make 6 equal deposits to the account, one deposit in each year from now until his daughter starts college. These deposits will begin today and will earn 8 percent interest, compounded annually.

a) What will be the present value of the cost of 4 years of education at the time the daughter becomes 18?b) What will be the value of the \$7,500 that the daughter received from her grandfather’s estate when she starts college at age 18?c) If the father is planning to make the first of 6 deposits today, how large must each deposit be for him to be able to put his daughter through college?3) “SRK Airport” authority issued a series of 3.4 percent 30-year bonds in February 2012. Interest rates rose substantially in the following years of the issue and made the price of the bond declined. 13 years later, In February 2025 the price of the bond has dropped from \$1000 to \$675. Assume that the bond requires annual interest payments.

d) What is yield to maturity of the bond? (Par value= \$1000 in 2012) e) Calculate the yield to maturity in February 2025. f) If interest rate stabilizes after 2025 and remains same for the reminder of the life of the bonds, what will be the bonds price in 2040, two years before maturity. g) What is the bond price during maturity (in 2042)?h) Assuming the condition in part (c) what would have been the current yield of a “SRK Airport” bond in 2025 and in 2040? 4) In January 1, 2012, Anim purchased an outstanding Rosette Corporation bond that was issued on January 1, 2010. The Rosette Corporation bond has a 9.5 percent annual coupon and a 30-year original maturity (matures on December 2039). There is a 15-year call protection (until December 2014), after which time the bond can be called at 109 (109 percent of per or at \$1090).Interest rates have declined since the bond was issued, and the bond is now selling at 116.575 percent of par or at \$1,165.

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75. Anim wants to determine both the yield to maturity and the yield to call of this bond. (Note: during calculation of yield to call assume that the bond will be outstanding until the call date. Thus the investor will have received interest payments for the call protected period and then will receive the call price- in this case which is \$1090 on the call date).i) What is yield to maturity of the Rosette bond? What is its yield to call? j) If Anim purchase this bond, which return do you think anim would actually earn? Explain your answer.

k) If the bond had sold at a discount, would the yield to maturity or the yield to call have been more relevant?5) Mashrafee Inc. is expected to grow at a constant rate of 6 percent and its dividend yield is 7 percent. The company is about as risky as the average firms are in the industry. However, the company just successfully completed some R&D work that leads the company to expect that its earnings will grow at a rate of 50 percent this year and 25 percent the following year, after which growth should match the 6 percent industry average rate.

The last dividend paid (D0) was \$1.00. What is the value per share of the firm’s stock?6) You purchase a share of Kamal Corporation stock for \$21.40. You expect it to pay dividends of \$1.07; \$1.1449 and \$1.

2250 in years 1, 2 and 3 respectively and you expect to sell it at a price of \$26.22 at the end of 4 years.l) Calculate the growth rate in dividends and the expected dividend yield. m) Assume that the calculated growth rate (in a) is expected to continue, you can add the dividend yield to the expected growth rate to get the expected total rate of return. What is the stock’s expected total rate of return?

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