Question

A company has two investment opportunities: Alternative A returns $36,000 now, $20,000 in two years and $8,000 in four years. Alternative B returns $1,470 at the end of every month for four years. The required rate of return is 8.5% compounded semi-annually. Using the discounted cash flow (DCF) method, which alternative is preferable?

Answer 1

Annual Interest Rate = 8.50%
Semiannual Interest Rate = 8.50% / 2
Semiannual Interest Rate = 4.25%

Effective Annual Rate = (1 + Semiannual Interest Rate)^2 - 1
Effective Annual Rate = (1 + 0.0425)^2 - 1
Effective Annual Rate = 1.08681 - 1
Effective Annual Rate = 0.08681 or 8.681%

Monthly Interest Rate = (1 + Effective Annual Rate)^(1/12) - 1
Monthly Interest Rate = (1 + 0.08681)^(1/12) - 1
Monthly Interest Rate = 1.00696 - 1
Monthly Interest Rate = 0.00696 or 0.696%

Alternative A:

Present Value = $36,000 + $20,000/1.00696^24 + $8,000/1.00696^48
Present Value = $58,667.71

Alternative B:

Present Value = $1,470/1.00696 + $1,470/1.00696^2 + … + $1,470/1.00696^47 + $1,470/1.00696^48
Present Value = $1,470 * (1 - (1/1.00696)^48) / 0.00696
Present Value = $1,470 * 40.68598
Present Value = $59,808.39

Alternative B is preferable as its present value is higher.