Question

a) What is the present value of $1,200 per year, at a discount rate of 8 percent, if the first payment is received 9 years from now and the last payment is received 28 years from now?

b) ABC Co. wants to sell you an annuity that will pay you $500 per quarter for 25 years. You want to earn a minimum rate of return of 5.1 percent. What is the most you are willing to pay today to buy this annuity?

c) You are scheduled to receive annual payments of $4,000 for each of the next 8 years. The discount rate is 8 percent.

Part 1: What is the present value if you receive these payments at the beginning of each year rather than at the end of each year?

Part 2: What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

d) Prepare an amortization schedule for a five-year loan of $60,000. The interest rate is 7 percent per year, and the loan calls for equal annual payments.

Answer 1

a. Present Value of Annual Cash Flow = (Annual Cash Flow in Year 9 ) * PVAF(0.08,20)/ (1 + Interest)^9

Present Value of Annual Cash Flow = 1200 * 9.8181/ (1 + 0.08)^9

Present Value of Annual Cash Flow = 11781.78/ 1.9990

Present Value of Annual Cash Flow = $5893.82

b. Amount willing to Pay Now = Quarterly Cash Flow * PVAF(0.051/4,25*4)

Amount willing to Pay Now = $500 * 56.3379

Amount willing to Pay Now = $28168.93

c. Present Value if the cash flow received at the end of year = Cash Flow * PVAF(0.08,8)

Present Value if the cash flow received at the end of year = 4000 * 5.7466

Present Value if the cash flow received at the end of year = $22986.56

Present Value if the cash flow received at the Beginning of year = Cash Flow * PVAD(0.08,8)

Present Value if the cash flow received at the Beginning of year = 4000 * 6.2064

Present Value if the cash flow received at the Beginning of year = $24825.48

Part 2: What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

Difference = $24825.48 - 22986.56 = $1838.92

d) Prepare an amortization schedule for a five-year loan of $60,000. The interest rate is 7 percent per year, and the loan calls for equal annual payments.

Annual payment = Loan / PVAF(0.07,5) = $60000 / 4.1002 = $14633.44

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