Chapter 9.M, Problem M.6P

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.

To calculate:

A schedule by showing its effect on current earnings through hedging relationship.

Answer to Problem M.6P

Total net loss from call option B is $\$900$ , net gain from put option C is

$\$99,600$ and net interest swap rate is $\$173,334$ .

Explanation of Solution

Calculation of change in time value excluded from effectiveness as follows:

  $\begin{array}{c}\text{Change in time value }\left(\text{July}\right)=\text{Time value at the end}-\text{Time value at the beginning}\\ \begin{array}{l}=\$2,400-\text{\$}2,000\hfill \\ =\$400\hfill \end{array}\end{array}$

Note:

Consecutively for next months

Call option B

Particulars	July (in $)	August (in $)	September (in $)	Total(in $)
Unrealized gain (loss):
$\begin{array}{l}\left(\$900-\$1,100\right)\hfill \end{array}$	$\left(200\right)$			$\left(200\right)$
$\left(\$600-\$900\right)$		$(300)$		$(300)$
$\left(\$200-\$600\right)$			$\left(400\right)$	$\left(400\right)$
Net gain (loss)	$\left(200\right)$	$(300)$	$\left(400\right)$	$\left(900\right)$

Calculation of unrealized gain (loss) as follows:

  $\begin{array}{c}\text{Unrealized gain}\left(\text{loss}\right)\text{on July}=\text{Value of option on July 31}-\text{Value of option on July 1}\\ \begin{array}{l}=\$900-\$1.100\hfill \\ =\left(\$200\right)\hfill \end{array}\end{array}$

Note:

Hedge is not effective which does not quality for special hedge.

Put Option C

Particulars	July (Amount be $)	August (Amount in $)	September (Amount In $)	Total (Amount be $)
Sales revenue			$287,500$	$287,500$
Cost of sales			$\left(200,000\right)$	$\left(200,000\right)$
Adjustment to cost of sales — Intrinsic value at July 1 of $0 versus intrinsic value at  $\frac{9}{10}\text{of}\$12,500$  $\left[10,000\times \left(\$30-\$28.75\right)\right]$			$12,500$	$12,500$
Gross profit on sales			$100,000$	$100,000$
Change in time value excluded from effectiveness.
Time value of   $\$500$at beginning vs.   $\$600$at the end	$100$			$100$
Time value of   $\$600$at beginning vs.   $\$200$at the end		$\left(400\right)$		$\left(400\right)$
Time value of   $\$200$at beginning vs.   $\$100$at the end			$\left(100\right)$	$\left(100\right)$
Net gain (loss)	$100$	$\begin{array}{l}\left(400\right)\hfill \end{array}$	$99,900$	$99,600$

Working note:

Calculation of adjustment to cost of sales as follows:

  $\begin{array}{c}\text{Adjustment to cost of sales}=\text{Number of units}\times \left(\text{Spot price on July}-\text{Spot price on September}\right)\\ =10,000\times \left(\$30-\$28.75\right)\\ =\$12,500\end{array}$

Futures contract D

Particulars	July (Amount in $)	August (Amount in $)	September (Amount in $)	Total (Amount in $)
Change in the time value excluded from effectiveness:  $\begin{array}{l}\left[\left(\$9.94-\$9.95\right)\text{Vs}.\left(\$9.90-\$59.92\right)\times 10,000\right]\\ \left[\left(\$9.90-\text{\$}9.92\right)\text{Vs}.\left(\$9.87-\$9.89\right)\times 10,000\right]\\ \left[\left(\$9.87-\$9.89\right)\text{Vs}.\left(\$9.84-\$89.85\right)\times 10,000\right]\end{array}$	$100$		$\left(100\right)$	$\left(100\right)$
Net gain (loss)	$100$		$\left(100\right)$

Note:

Numbers of units is 10,000 future prices of $10per unit.

Interest rate swap:

Particulars	July (Amount in SI	August (Amount in $)	September (Amount in SI	Total (Amount in S)
Variable interest income
$\left(6.8\%\times \$\mathrm{10.000.000}\times \frac{1}{2}\right)$	$56,667$			$56,667$
$\left(6.8\%\times \$\mathrm{10.000.000}\times \frac{1}{2}\right)$		$56,667$		$56,667$
$\left(6.7\%\times \$\mathrm{10.000.000}\times \frac{1}{2}\right)$			$55,833$	$55,833$
Settlement of fixed variable difference:
$\left[\left(7\%-6.8\%\right)\times \$10,000.000\times \frac{1}{2}\right]$		$1,667$		$1,667$
$\left[\left(7\%-6.7\%\right)\times \$10,000.000\times \frac{1}{2}\right]$			$2,500$	$2,500$
Net interest Income	$56,667$	$58,334$	$58,333$	$173,334$

Note:

LIBOR for July is $6.8\%$

LIBOR for August is $6.8\%$

LIBOR for September is $6.7\%$

Fixed rate of interest is $7\%$

Conclusion

Total net loss from call option B is $\$900$ , net gain from put option C is $\$99,600$ and net interest swap rate is $\$173,334$ .