Question

McGilla Golf has decided to sell a new line of golf clubs. The company would like to know the sensitivity of NPV to changes in the price of the new clubs and the quantity of new clubs sold. The clubs will sell for $795 per set and have a variable cost of $355 per set. The company has spent $200,000 for a marketing study that determined the company will sell 65,000 sets per year for seven years. The marketing study also determined that the company will lose sales of 11,000 sets of its high-priced clubs. The high-priced clubs sell at $1,165 and have variable costs of $625. The company will also increase sales of its cheap clubs by 13,000 sets. The cheap clubs sell for $385 and have variable costs of $175 per set. The fixed costs each year will be $10,050,000. The company has also spent $1,500,000 on research and development for the new clubs. The plant and equipment required will cost $37,800,000 and will be depreciated on a straight-line basis. The new clubs will also require an increase in net working capital of $2,200,000 that will be returned at the end of the project. The tax rate is 25 percent, and the cost of capital is 13 percent. What is the sensitivity of the NPV to each of these variables? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) ΔΝPV/ΔΡ ΔΝPV/ΔQ

Answer 1

Price of new Clubs	$795	Expected unit Sales per year	65,000	for seven years
Price of high-priced Clubs	$1,165	Expected unit Sales Loss per year	(11,000)
Price of Cheap Clubs	$385	Expected unit Sales increase per year	13,000

Variable Cost of New Clubs	$355
Variable Cost of high-priced Clubs	$625
Variable Cost of Cheap Clubs	$175
Cost of Marketing Study	$200,000
R&D Cost (one-time)	$1,500,000
Fixed Cost (per year)	$10,050,000
Cost of Plant & Equipment	$37,800,000
Increase in net working capital	$2,200,000

Tax Rate	25%
Cost of Capital	13%
Life of Project	7 years

Let us start the calculation to find out the project of the new project - sales of new clubs

		Calculation Formula	Calculation Step
Revenue (new clubs) per year	$51,675,000	Price of new Clubs X Units Sales per year	795 * 65000
Revenue from cheap clubs	$5,005,000	Price of cheap Clubs X Unit Sales per year	385*13000
Revenue Loss from high-priced Clubs	($12,815,000)	Price of high-priced Clubs X Unit Sales Loss per year	- 1165 * 11000
Extra Variable Cost (New Clubs)	$23,075,000	Variable Cost X Unit Sales per year	355 * 65000
Extra Variable Cost (Cheap Clubs)	$2,275,000	Variable Cost X Unit Sales per year	175 * 13000
Variable Cost Savings (high-priced) Clubs	($6,875,000)	Variable Cost X Unit Sales per year	- 625 * 11000
Depreciation per year	$5,400,000	Cost of Plant & Equipment/ no of years	37,800,000/7

Calculating the P&L Statement for the year

Revenue per year (R)	$43,865,000	Sum of the revenues calculated in above table
Variable Expenses (V)	($18,475,000)	Sum of the variables costs calculated above
Fixed Cost per year (FC)	($10,050,000)
Depreciation (D)	($5,400,000)
Profit Before Tax (PBT)	$9,940,000	PBT = R-V-D-FC
Taxes (Tax)	($2,485,000)	Tax = Tax Rate X PBT
Profit After Tax (PAT)	$7,455,000	PAT = PBT - Tax

In the above table, only depreciation is a non-cash item.
Thus, cash PAT = PAT + depreciation = $7,455,000 + $5,400,000 = $12,855,000

Preparing the cash flow table

Year 0	($41,700,000)	Cost of R&D, Cost of Marketing Study, Cost of Plant & Equipment, Increase in et orking Capital
Year 1	$12,855,000	Cash PAT
Year 2	$12,855,000	Cash PAT
Year 3	$12,855,000	Cash PAT
Year 4	$12,855,000	Cash PAT
Year 5	$12,855,000	Cash PAT
Year 6	$12,855,000	Cash PAT
Year 7	$15,055,000	Cash PAT + release of net working Capital
NPV	$14,236,983	Calculated using excel function

Now we can calculate the sensitivity of the NPV to the two factors - tax rate and cost of capital.
If tax rate increases by 1% to 26%, what changes in the above calculations is the taxed paid and thus the PAT and the cash PAT.
If we redo all the above calculations in a spreadsheet,

NPV (26% tax rate) = $13,849,950
Thus, NPV sensitivity to tax rate = ($13,849,950- $14,236,983) = (- $389,033)

Similarly, if we make the above calculations using a cost of capital of say 14% instead of 13%,
NOV (14% cost of capital) = $12,548,562
Thus, NPV sensitivity to cost of capital = ($12,548,562- $14,236,983) = (- $1,688,421)