Chapter 9.M, Problem M.3P

To determine

Hedging:

Hedging against an investment risk is termed for strategically implementing the instruments and tools in the market to minimize the risk and effects of any adverse price movements. It can be said that investors are benefitted through hedging as they hedge one investment by making another investment. The financial instruments like exchange traded funds, stocks, forward contracts, options, insurance, swaps, etc may construct hedge.

To calculate:

The effect on earnings for 3 months from January to March for various hedging instruments.

Answer to Problem M.3P

Fair value of Contract in March is $ $600$ depending on Number of units as well as future prices of February and March. Moreover Net impact on earnings changes for Forward contract and Call Option.

Explanation of Solution

Working notes:

Calculation of Fair value of Contract:

  $\begin{array}{c}\text{Fair Value of Contract in March}=\text{Number of Units}\times \left(\begin{array}{l}\text{Future Price Per unit on February}\\ -\text{Future Price per Unit in March}\end{array}\right)\\ =10,000\text{units}\times \left(\$3.50-\$3.44\right)\\ =\$600\end{array}$

Note:

The difference between change in fair value and change in intrinsic value is considered as change in time value.

Forward Contract to buy:

Particulars	January(Amount in $)	February(Amount in $)	March(Amount in $)
Number of units per contractSpot Price per unitForward rate per unitOriginal forward rate per unit	$\begin{array}{l}5,000\text{units}\\ 90.12\\ 91.50\\ 92.00\end{array}$	$\begin{array}{l}5,000\text{units}\\ 90.50\\ 91.20\\ 92.00\end{array}$	$\begin{array}{l}5,000\text{units}\\ 90.60\\ 91.60\\ 92.60\end{array}$
Fair Value of Forward in Futures:Original Forward value  $\left(5000\times \$92\right)$Current Forward Value  $\begin{array}{l}\left(5000\times \$91.50\right)\\ \left(5000\times \$91.20\right)\\ \left(5000\times \$60.60\right)\end{array}$	$\begin{array}{l}460,000\\ 457,500\end{array}$	$\begin{array}{l}460,000\\ 456,000\end{array}$	$\begin{array}{l}460,000\\ 453,000\end{array}$
Change in forward value-Gain(Loss)	$\left(2,500\right)$	$\left(4,000\right)$	$\left(7,000\right)$
Discount Rate		$6\%$
Present Value of the fair value:   $\begin{array}{l}FV=\left(\$2,500\right),n=1.5,I=0.25\%\\ FV=\left(\$4,000\right),n=0.5,I=0.25\%\\ FV=\left(\$7,000\right),n=0.0,I=0.25\%\end{array}$Current present Value (A)Prior Present Value (B)	$\left(2,491\right)$  $\left(2,491\right)$	$\begin{array}{l}\left(3,995\right)\\ \left(7,000\right)\\ \left(3,995\right)\\ \left(2,491\right)\end{array}$	$\begin{array}{l}\left(7,000\right)\\ \left(3,995\right)\end{array}$
Change in Present Value	$\left(2,491\right)$	$(1,504)$	$(3,005)$
Effect on earnings − Gain(Loss)Gain(Loss) on firm commitmentGain(Loss) on forward contractSales revenueCost of sales	$\begin{array}{l}2,491\\ \left(2,491\right)\end{array}$	$\begin{array}{l}1,504\\ (1,504)\end{array}$	$\begin{array}{l}3,005\\ (3,005)\\ \left(443,000\right)\\ 360,000\end{array}$
Net Impact on earnings	$$  $0$	$0$	$\left(83,000\right)$

Working Notes:

Calculation of Sales Revenue:

  $\begin{array}{c}\text{Sales Revenue}=\left(\text{Number of units}\times \text{Selling Price per unit}\right)-\text{Gain On Commitment}\\ =\left(5000\text{units}\times \$90\right)-\$7000\\ =\$443,000\end{array}$

Call Option:

Particulars	January(Amount in $)	February(Amount in $)	March(Amount in $)
Number of Units Per OptionSpot Price Per unitFutures Price Per unit	$100,000$ units   $8.05$   $8.00$	$100,000$ units   $8.02$  $8.00$	$100,000$ units   $7.95$  $8.00$
Fair value of option Value of Option: Intrinsic Value   $\left[100000\ast \left(\$8.02-\$8.00\right)\right]$Out of the moneyTime Value	$2,400$   $2,000$   $400$	-	-
Total Value	$2,400$	-
Effect on earnings-Gain(Loss): Change in time value- Gain(Loss)Original value of$   $1000$ Vs. $   $400$$   $400$Vs. $   $0$Change in Intrinsic Value-Gain(Loss)$   $5000$ Vs. $   $2000$$   $2000$Vs. $   $0$Sales RevenueCost of Sales (Processing)Cost of Sales (Commodity A)Change in intrinsic value previously in OCIOriginal Intrinsic value of $   $5000$Vs. $   $0$	$(600)$	$(400)$	$1,200,000$ (   $110,000$) (   $795,000$)(   $5,000$)   $$
Net Impact on Earnings	$(600)$	$(400)$	$290,000$

Working Notes:

Calculation of Sales Revenue:

  $\begin{array}{c}\text{Sales Revenue}=\text{Number of units}\times \text{Selling Price per unit}\\ =100,000\text{units}\times \$12\\ =\$1,200,000\end{array}$

Calculation of cost of sales processing:

  $\begin{array}{c}\text{Cost of Sales}=\text{Number of units}\times \text{Processing Cost per unit}\\ =100,000\text{units}\times \$1.10\\ =\$110,000\end{array}$

Calculation of Cost of sales- Commodity A:

  $\begin{array}{c}\text{Cost of Sales}=\text{Number of units}\times \text{Price per unit}\\ =100,000\text{units}\times \$7.95\\ =\$795,000\end{array}$

Conclusion:

Fair value of Contract in March is $\$600$ depending on Number of units as well as future prices of February and March.