Question

Q 42,43,44,45,47

CHAPTER 6 The Time Value of Money 219 Perpetulties 6-42. Calculating the present value of a perpetuity) (Related to Checkpoint page 206) What is the present value of the following? a. A $300 perpetuity discounted back to the present at 8 percent b. A $1,000 perpetuity discounted back to the present at 12 percent C. A $100 perpetuity discounted back to the present at 9 percent d. A $95 perpetuity discounted back to the present at 5 percent C. A $100 per peruity discount Back to the press 6-43. (Calculating the present value of a perpetuity What will be the present perpetual payment of £400 per year if the applicable discount rate is 6 perce will be its value if the discount rate is changed to 3 percent able discount rate is 6 percent? What 6-44. (Calculating the present value of a growing perpetuity) (Related to Checkp on page 207) A perpetuity pays $1,000 at the end of Year 1. and the annual cash perpetuity) (Related to Checkpoint 6.5 flows grow at a rate of 4 percent per year indefinitely. What is the present value if the appropriate discount rate is 8 percent? If the appropriate discount rate is 6 percent? 6-45. (Calculating the present value of a growing perpetuity) A pension plan pays €30,000 at the end of Year 1 and then grows at the rate of 3 percent per year indefi- nitely. What is the present value if the rate of interest to discount the cash flow is 7 percent? 646. Calculating the present value of a growing perpetuity) Jonathan Lee wants to start an annual bursary of €50,000 for his alma mater in Berlin. The first payment will occur at the end of this year and it will then grow by 5 percent each year to cover for infla- tion. If the bank account pays 8 percent per annum, how much does Jonathan needs to invest now to support this bursary forever? 5 47. (Calculating the present value of a negatively growing perpetuity) Your firm has taken cost-saving measures that will provide a benefit of $10,000 in the first year. These cost savings will decrease each year at a rate of 3 percent forever. If the appro- priate interest rate is 6 percent, what is the present value of these savings? Complex Cash Flow Streams 48. (Calculating the present value of annuities and complex cash flows) (Related to Checkpoint 6.6 on page 209) You are given three investment alternatives to analyze. The cash flows from these three investments are as follows: A $10.000

Answer 1

Solution :-

6-42 • perpetuity Present Value of a Perpetuity discount rate Present Value – $300 a $3750 0.08 Present Value = $1000 0.12 - $8333.33 to present Value - $100 - $111. 11 0.09 to present Value - $95 - $ 1900 O.OS

6-43 year Perpetuity - discount rate = £ yoo per 6% of 0.06 Present Value & Perpetuity discount rate £400 – £ 6666.67 0.06 If discount rate is 3% of 0.03 then. Present Value = £400 – £13333.33 0.03 6-44 Perpetuity Payment & $1000 Growth rate (g) = 4% or 0.04 discount rate (8) = 8% of 0.08 Present value - Perpetuity of a growing perpetuity Payment at the end of year 1 $1000 0.08-0.04 - $1000 0.04 $ 25000

If the discount rate (8) = 6% of 0.06 then, Present Value of growing perpetuity - $1000 = $1000 – $ 500oo. 0.06-0.04 6-45 Cash Flow at Year 1 - €30000 Growth rate (g) = 3% of 0.03. discount rate (8) = 7% or 0.07 Now, Present Value of growing - Cash Flow at year 4 r- g perpetuity €30000 0.07-0.03 € 30000 0.04 - €750000

6-47- - expected Benefit = $ 10000 Crowth rate (g) = -3% 08-0.03 Interest rate (2) = 6% OF 0.06. Now, Present value of Savings (decreasing) Expected benefit r- g $10000 0.06-(-0.03) $10000 0.06 +0.03 $ 10000 0.09 - $11111111