Question

An investment offers €10,000 per year for 15 years, with the first payment occurring one year from now. If the required return is 10 per cent,

a) What is the value of the investment?

b) What would the value be if the payments occurred for 50 years?

c) For ever?

Answer 1

Payment per year = €10,000

Number of periods = 15 years

The cash flows are as follows:

Solution 1) Use the following formula to find the Present Value (PV):

PV=P*{1- 1 / [1 + R]^N} / R

P = Payment per year = €10,000

N = Number of periods = 15

R = Interest rate = 10%

PV =10000 * {[1 - 1/ [1+10%]^15} / 10%

PV = 10000* {[1 - 1/[1+0.1]^15}/10%

PV = 10000*(1 - 1/(1.1)^15)/10%

PV = 10000*(1 - 0.239392)/10%

PV = 10000*(0.76060795)/10%

PV = 7606.0795/10%

PV = 76060.795 = €76,060.80

Solution 2) If number of years, N = 50

Use the same formula as above but change the exponent to 50 years and you should get:

PV=P*{1- 1 / [1 + R]^N} / R

PV =10000 * {[1 - 1/ [1+10%]^50} / 10%

PV = 10000*[1 - 0.0085186]/10%

PV = 10000*0.991481449/10%

PV = 9914.81449/10%

PV = 99148.1449

PV = €99,148.14

Solution 3) If the cash flows will be received forever, then, it will become the case of perpetuity

Present value (PV) of perpetuity = payment per period/Interest Rate

PV = 10000/10%

PV = €100,000

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