Question

A piece of land can be purchased by paying $50 000 cash or $20 000 deposit and two equal payments of $20 000 at the end of 2 years and 4 years respectively. To pay cash, the buyer would have to withdraw the money from an investment earning interest at j2 = 8% (i.e. 8% p.a. compounded twice per year). Which option is better and by how much, in present value terms?

Answer 1

First Alternative: Payment of $50,000 cash. So, its present worth is $50,000

Second Alternative: Down payment of $20,000, and two equal payments of $20,000 at the end of 2 years and 4 years respectively.

Interest rate (i) = 8% or 0.08 per annum

Present Worth = $20,000 + $20,000(P/F, 8%, 2) + $20,000(P/F, 8%, 4)

Present Worth = $20,000 + $20,000/(1 + 0.08)² + $20,000/(1 + 0.08)⁴

Present Worth = $51,846

Since, the present worth of the second alternative is higher than that of the first alternative, so first alternative of cash payment of $50,000 should be selected.