Question

An investor is hesitating between two projects. The first will yield steady returns of X every 6 months for 10 years. The second will return 1000 per month for 5 years, then will yield 500 per month in perpetuity. If the effective annual rate is 10%, for what X would the investor be indifferent between the two projects ?

Answer 1

P1 = Cash Flows for first project = X

n1 = 10*2 = 20 semi annual compoundings

r1 = semi annual interest rate = 10%/2 = 5%

r2 = monthly interest rate = 10%/12 = 0.83333333%

P2 = Cash Flow per month = 1000

P3 = Cash Flow per month = 500

n2 = 5*12 = 60 months

Present value of Cash flows of first one = Present value of Cash flows of Second one

P1 * [1 - (1+r1)^-n1] / r1 = [P2 * [1 - (1+r2)^-n2] / r2] + [(P3 / r2) / (1+r2)^n2]

x * [1 - (1+5%)^-20] / 5% = [1000 * [1 - (1+0.83333333%)^-60] / 0.83333333%] + [($500 / 0.83333333%) / (1+0.83333333%)^60]

x * 0.623110517 / 0.05 = [1000 * 0.392211288 / 0.0083333333] + [$60,000 / 1.64530861]

x * 12.4622104 = 47,065.3547 + 36,467.3227

x * 12.4622104 = 83,532.6774

x = 6,702.87812

Therefore, Value of x is 6,702.88 would be indifferent between the two projects