You are offered GHc900 five years from now or GHc150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept?

Question

1.     You are offered GHc900 five years from now or GHc150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? Why are your answers different?

Answer 1

The question is comparing two cash flows to determine the one with the higher return above a threshold.

To find the present value of this lump sum, we'll use the present value formula:

PV = FV / (1 + r)^n

Where:

FV (Future Value) = GHc900

r (interest rate) = 6% = 0.06

n (number of years) = 5

PV = 900 / (1 + 0.06)^5

= 900 / 1.33823

= GHc672.43

Option 2: GHc150 annually for five years

For this option, we need to calculate the present value of an annuity. We can use the present value of annuity formula:

PV = PMT * [1 - (1 + r)^-n] / r

Where:

PMT (Payment) = GHc150

r (interest rate) = 6% = 0.06

n (number of years) = 5

PV = 150 * [1 - (1 + 0.06)^-5] / 0.06

= 150 * 4.2124

= GHc631.86

Comparison

Option 1 (Lump sum): GHc672.43

Option 2 (Annuity): GHc631.86

The lump sum option has a higher present value, so it would be the better choice financially.

Therefore, accept the offer of GHc900 five years from now, as it has a higher present value (GHc672.43) compared to the annuity option (GHc631.86) when discounted at 6% interest.