Explain this question to me (Question #77, GARP Practice Test)

I don’t understand why they subtract K from the forward price in the calculation. Couldn’t you just discount 1050 back 9 months to get to today’s price?

Three months ago, a company entered in a one-year forward contract to buy 100 ounces of gold. At the
time, the one-year forward price was USD 1,000 per ounce. The nine-month forward price of gold is now
USD 1,050 per ounce. The continuously-compounded risk-free rate is 4% per year for all maturities, and
there are no storage costs. Which of the following is closest to the value of the contract?
a.
b.
c.
d.
USD 1,897
USD 4,852
USD 5,000
USD 7,955
Explanation: The forward price is computed as follows:
F 0 = 100 x (F 0 - K)e -rT
F 0 = 1,050
K = 1,000
r = 0.04
T = 0.75
F = 100 x (1050 - 1000)e -0.04*0.75 = 4,852

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The question asks you the value of the position not the price of the forward contract.

Long position = paying 1000/ounce of gold vs paying 1050/ounce of gold at maturity if bought the new forward —> net benefit of 50/ounce of gold

PV of net benefit vs current price —-> PV of 50.

Mkt price of your forward has increased so your position has a +value as you bought cheaper than the current mkt price.

—OR—

Discount original forward contracts held = 970.4455 (PV or price of your long forward)

Discount 9mnth forward in the market now to today = 1018.9678 (PV or price of entering into a new forward today expiring with original forward)

The contracts you hold (long position) at 970 vs what their current mkt price is 1018.9 (potential sale price)—>value of your position is higher as now the same contract is available for a higher price.

Value of position held = 1018.9678 - 970.4455 = 48.52 *100 = 4852

Hope this helps!