Question

ABC is considering two investment alternatives. Alternative A requires an initial investment
of $10,000; it will yield incomes of $3000, $3500, $4000, and $4500 over its 4-year life.
Alternative B requires an initial investment of $12,000; it is anticipated that the revenue
received each year will increase at a rate of 10%/year (each year’s revenue is 10% higher than
that of the preceding year).
Based on an interest rate of 12% compounded annually, what must be the revenue at the first
year for B in order for alternatives A and B to be equivalent? (Draw the cash flow profiles)

Answer 1

Alternative A

Initial investment = $10000

Revenue

Year 1 = 3000

Year 2 = 3500

Year 3 = 4000

Year 4 = 4500

Present value of investment A using NPV calculator is:

Present value of investment A is $ 1175.70

Investment B

Let Revenue = X

Initial investment = 12000

Revenue

Year 1 = X

Year 2 = X * ( 1 + 10% ) = 1.10 X

Year 3 = X * ( 1 + 10% ) ^ 2 = 1.21 X

Year 4 = X * ( 1 + 10% ) ^ 3 = 1.33 X

Present value of cash flows

Year 1 = X / ( 1 + 12%) = 0.89 X

Year 2 = 1.10 X / ( 1 + 12%) ^ 2 = 0.88 X

Year 3 = 1.21 X / ( 1 + 12%) ^ 3 = 0.86 X

Year 4 = 1.33 X / ( 1 + 12%) ^ 4 = 0.84 X

For both the alternatives to be equivalent:

X * ( 0.89 + 0.88 + 0.86 + 0.84 ) - 12000 = 1175.7

3.47 X = 13175.7

X = 3797.03

Thus for both the alternatives to have the same present value, First year revenue = $ 3797.03

Cash flow profiles

Year 1 = 3797.03

Year 2 = 4176.73

Year 3 = 4594.40

Year 4 = 5053.84