Question

5. This question consists of three parts. When performing the calculations, keep as many decimal places as you can for intermediate answers, but round your final answers to two decimal places.             (7 marks total)

1. You have taken out a loan that requires you to repay $200 per month for 10 years at 12% annual percentage rate with monthly compounding. The first payment occurs today. What is the current value of this loan?        (2 marks)
2. You have purchased a three-year inflation-indexed investment. This investment will pay you $X every six months, with each payment adjusted upward for inflation. Let’s say that the proposed first payment is $300 (before inflation adjustment), the average forecasted inflation rate will be 0.5% every six months for the next three years, and your required annual rate of return is 6% (compounded semi-annually). What is the present value of this inflation-indexed investment? (Hint: You cannot use a financial calculator to solve this problem.)                                                  (4 marks)

c) You have purchased an investment that promises to pay you a constant $300 every six months, indefinitely. Your required annual rate of return is 6%, compounded semi-annually; assume that this rate will be the same indefinitely. What is the present value of this investment three years from now? (Hint: You cannot use a financial calculator to solve this problem.)

Answer 1

a)

PMT = 200
Nper = 10 * 12 = 120
Rate = 12% / 12 = 1%
FV = 0

Current value of loan can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(1%,120,-200,0)
= $13,940.10

b)
Present value of investment = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n)
= (300 / (0.03 - 0.005)) * (1 - ((1+0.005)/(1+0.03))^6)
= (300 / 0.025) * (1 - 0.862924942)
= 12,000 * 0.137075057
= $1,644.90

c)
Present value of investment = P / r
= $300 / 0.03
= $10,000.