Confused about Troubadour's short position

Position 3 : Troubadour holds a short position in a yen/US dollar forward contract with a notional value of $1,000,000. At contract initiation, the forward rate was ¥112.10 per $1. The forward contract expires in three months. The current spot exchange rate is ¥112.00 per $1, and the annually compounded risk-free rates are –0.20% for the yen and 0.30% for the US dollar. The current quoted price of the forward contract is equal to the no-arbitrage price.

Question : The value of Position 3 is closest to:

Correct Answer: ¥239,963.

The current no-arbitrage price of the forward contract is ¥111.8602

If the dude is short yen/usd, he is short YEN. (CFAI curriculum states that in currency forwards/futures use the convention is DC/FC).

How is it possible that the position has positive value? If he has agreed to sell 112.10JPY to get 1 USD while the current price of the contract is 111.8602JPY for 1 USD, doesn’t his position have a negative value?

You will want to divided by the risk free rate of japan, which is negative.

Vt=PV{Ft(T)-F0(T)} Long Position Present Value of the differences in the Forward rates

Vt=PV{F0(T)-Ft(T0)} Short Position

if you no how to calculate no arbitrage forward price at the time 0 and the forward price at time t then find their difference and discount them using the rate for the price currency this should be easy as ABC

Yeah thanks for the answers but I wasn’t asking about the technical side of the solution. My question was : How is it possible that the position has _ positive _ value? If he has agreed to sell 112.10JPY to get 1 USD while the current price of the contract is 111.8602JPY for 1 USD, doesn’t his position have a _ negative _ value?

From CFAI : ‘‘We use the shorthand notation of DC/FC to refer to the price of one unit of foreign currency expressed in terms of domestic currency units when embedded in an equation.’’