Calculate the present value of each of the following future payments. a) What is

Question

Calculate the present value of each of the following future payments.

a) What is the present value of receiving $200 one year from now when the prevailing rate of interest is 8 percent?

b) What is the present value of $200 to be paid to you at the end of two years, if the market interest rate is 5 percent?

c) If you are to receive a payment of $200 at the end of the first year and a payment of $250 at the end of the second year and the market interest rate is 5 percent, what is the present value of this income stream?

d) If the discount rate is 5 percent, the present value of annual $100,000, what is the payment in perpetuity?

Explanation / Answer

(a) Present value (PV) = Future value (FV) / (1 + Interest rate)Number of years

= $200 / 1.08

= $185.19

(b) PV = $200 / (1.05)2 = $200 / 1.1025 = $181.41

(c) PV ($) = [200 / 1.05] + [250 / (1.05)2] = 190.48 + (250 / 1.1025) = 190.48 + 226.76

= 417.24

(d) For a perpetuity,

Present value = Annuity / Discount rate

= $100,000 / 0.05

= $2,000,000

I.e. If annual annuity is $100,000 then its present value is $2,000,000.

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