Question

7. An investment has a cost of $2000. The investment will have a payout of X at the end of the first year. This initial payout X will grow at the rate of 10% per year for the next 3 years, then by 6% per year for the next 2 years, and then at the rate of 4% per year for the following 1 year. You believe the riskiness of this investment is 9%.

a. Calculate the smallest X that would entice you to invest.

Answer 1

Present Value of the payouts must at least equal cost i.e., 2000

Hence,
I have just taken the present value of the cash flows in this manner

X/1.09+X/1.09*(1.1/1.09)^1+X/1.09*(1.1/1.09)^2+X/1.09*(1.1/1.09)^3+X/1.09*(1.1/1.09)^3*(1.06/1.09)+X/1.09*(1.1/1.09)^3*(1.06/1.09)^2+X/1.09*(1.1/1.09)^3*(1.06/1.09)^2*(1.04/1.09)=2000

=>X=2000/(1/1.09+1/1.09*(1.1/1.09)^1+1/1.09*(1.1/1.09)^2+1/1.09*(1.1/1.09)^3+1/1.09*(1.1/1.09)^3*(1.06/1.09)+1/1.09*(1.1/1.09)^3*(1.06/1.09)^2+1/1.09*(1.1/1.09)^3*(1.06/1.09)^2*(1.04/1.09))

=>X=313.48

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