Question

McGilla Golf has decided to sell a new line of golf clubs. The clubs will sell for $844 per set and have a variable cost of $427 per set. The company has spent $189951 for a marketing study that determined the company will sell 5446 sets per year for seven years. The marketing study also determined that the company will lose sales of 934 sets of its high-priced clubs. The high-priced clubs sell at $1023 and have variable costs of $707. The company will also increase sales of its cheap clubs by 1130 sets. The cheap clubs sell for $412 and have variable costs of $253 per set. The fixed costs each year will be $877567. The company has also spent $111774 on research and development for the new clubs. The plant and equipment required will cost $2858196 and will be depreciated on a straight-line basis. The new clubs will also require an increase in net working capital of $132915 that will be returned at the end of the project. The tax rate is 34 percent, and the cost of capital is 8 percent. What is the sensitivity of the NPV to changes in the price of the new clubs? [Hint: Think of this as, "How much will NPV change if I increase the price of the new clubs by $1?"] (Do not round intermediate calculations and round your final answer to the nearest dollar. Omit the "$" sign and commas in your response. For example, $12,345.6789 should be entered as 12346.)

Answer 1

First, we compute the NPV normally using the given data -

Initial Investment = Plant and Equipment cost + Net working capital required = $2,858,196 + $132,915 = $2,991,111

Marketing study and research and development costs are sunk costs, so they will not be considered while computing NPV.

Annual OCF

Particulars	Amount ($)
Contribution from new clubs [ ($844 - $427) x 5446 ]	2,270,982
Less: Contribution lost on high priced clubs [ ($1023 - $707) x 934 ]	295,144
Add: Contribution from cheap clubs [ ($412 - $253) x 1130 ]	179,670
Less: Fixed costs	877,567
Less: Depreciation [ $2858196 / 7 ]	408,313.714285
Earnings before tax	869,627.28572
Less: Tax @34%	295,673.277144
Net Income	573,954.008576
Add: Depreciation	408,313.714285
Annual OCF	982,267.722861

NPV

Particulars	Year	Amount (a)	PVIF @8% (b)	Present Value (a x b)
Annual OCF	1-7	982,267.722861	5.20637005906	5,114,049.26228
Add: Working Capital recovered	7	132,915	0.58349039523	77,554.62588
Total Present value of Cash Inflows				5,191,603.88816
Less: Initial Investment	0	2,991,111	1	2,991,111
NPV				2,200,492.88816

Now, lets say the price of new clubs is $850. We again compute NPV as above under this scenario assuming everything else remaining the same -

Annual OCF

Particulars	Amount ($)
Contribution from new clubs [ ($850 - $427) x 5446 ]	2,303,658
Less: Contribution lost on high priced clubs [ ($1023 - $707) x 934 ]	295,144
Add: Contribution from cheap clubs [ ($412 - $253) x 1130 ]	179,670
Less: Fixed costs	877,567
Less: Depreciation [ $2858196 / 7 ]	408,313.714285
Earnings before tax	902,303.28572
Less: Tax @34%	306,783.117144
Net Income	595,520.168576
Add: Depreciation	408,313.714285
Annual OCF	1,003,833.88286

NPV

Particulars	Year	Amount (a)	PVIF @8% (b)	Present Value (a x b)
Annual OCF	1-7	1,003,833.88286	5.20637005906	5,226,330.67199
Add: Working Capital recovered	7	132,915	0.58349039523	77,554.62588
Total Present value of Cash Inflows				5,303,885.29787
Less: Initial Investment	0	2,991,111	1	2,991,111
NPV				2,312,774.29787

Sensitivity = Change in NPV / Change in price of new clubs

or, Sensitivity = (2,312,774.29787 - 2,200,492.88816) / (850 - 844) = 18,713.568285 or 18714 [Also try 18713 in case you get incorrect answer]