Question

Brandon has almond orchards, but he prefers to eat walnuts instead.

His neighbor, an owner of the walnut orchard, has offered to swap this year’s crop with him. Assume Brandon produces 1000 tons of almonds today and his neighbor produces 700 tons of walnuts today. If the price of almonds is $100 per ton and the price of walnuts is $150 per ton. However, due to some financial constraint, his neighbor can only pay one-third of the income from his walnut crop to Brandon today. The rest (i.e. two-thirds of the income) will be paid in one year. Suppose bank's interest rate is 6% today.

What is the net present value of swapping with his neighbor?

Answer 1

Value of Almonds = 1000 tons * $100 = $100,000

Value of Walnuts = 700 tons * $150 = $105,000

Todays payment for Walnuts = $105,000 * 1/3 = $35,000

Payment in 1 year for Walnuts = $105,000 * 2/3 = $70,000

r = Interest rate = 6%

Present Value of Walnuts Payment = [$35,000 / (1+6%)^0] + [$70,000 / (1+6%)^1]

= $35,000 + $66,037.7358

= $101,037.74

Net Present Value = Present Value of Walnuts Payment - Value of Almonds

= $101,037.74 - $100,000

= $1,037.74

herefore, net present value of swapping with his neighbour is $1,037.74