Question

Consider an asset is priced at N$250,000. The risk-free interest rate is 8% per annum, and a futures contract on the asset expires in 75 days.

(a) Find the appropriate futures price if the future value of storage costs on the underlying asset at the futures expiration equals 0.3% of the present value of the underlying.

(b) Find the appropriate futures price if the future value of cash flows on the underlying asset equals N$71,500.

(c) Find the appropriate futures price if the future value of the net overall cost of carry on the underlying asset equals N$12,500.

Answer 1

(a)

Future Price = Current price x {1+ (rxt) } + Storage Coast

= N$250,000 x (1+ 0.08 x75/365) + N$250,000 x 0.3%

= N$250,000 x (1 + 0.01644) + N$750

= N$250,000 x 1.01644 + N$750

= N$254,110 + N$750

= N$254,860

(b)

Future Price = Current Price x {1 + (r x t) } - Future Cash flow

= N$250,000 x (1+ 0.08 x75/365) -N$71,500

= N$250,000 x (1 + 0.01644) + N$71,500

= N$250,000 x 1.01644 + N$71,500

= N$254,110 + N$71,500

= N$182,610

(Assumption : Ignoring the storage cost)

(c)

Future Price = Current Price + Net Overall carrying cost.

= N$250,000 + N$12,500

= N$262,500

(Assumption : Current price not multiply with interest cost as we assume that it include in net overall cost.)

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