Question

Needing help with portion b-3 and c. I have solved the other portions.

We are evaluating a project that costs $848,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 62,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $636,000 per year. The tax rate is 35 percent, and we require a return of 20 percent on this project.

a. Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Break-even point            units

b-1 Calculate the base-case cash flow and NPV. (Do not round intermediate calculations and round your NPV answer to 2 decimal places, e.g., 32.16.)

Cash flow	$
NPV	$

b-2 What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

ΔNPV/ΔQ          $  

b-3 Calculate the change in NPV if sales were to drop by 500 units. (Enter your answer as a positive number. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

NPV would  (Click to select)  increase  decrease  by $  

c. What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

ΔOCF/ΔVC          $

Answer 1

b-3.

Sales revenue for base case 62,000 units = $ 40 x 62,000 = $ 2,480,000

Variable cost for 62,000 units = $ 20 x 62,000 = $ 1,240,000

Sales revenue for 61,500 units = $ 40 x 61,500 = $ 2,460,000

Variable cost for 61,500 units = $ 20 x 61,500 = $ 1,230,000

Depreciation = Initial cost /useful life = $ 848,000/8 = $ 106,000

Computation of annual cash flow for both cases:

	For 62,000 units	For 61,500 units
Sales revenue	$        2,480,000	$          2,460,000
Less: Variable cost	$        1,240,000	$          1,230,000
Contribution	$        1,240,000	$          1,230,000
Less: Fixed cost	$            636,000	$              636,000
Operating profit	$            604,000	$              594,000
Less: Depreciation	$            106,000	$             106,000
Profit before tax	$            498,000	$              488,000
Less: Tax @ 35%	$            174,300	$              170,800
Profit after tax	$            323,700	$              317,200
Add: Depreciation	$            106,000	$              106,000
Annual cash flow	$            429,700	$              423,200

Computation of NPV for both cases:

			For 62,000 units		For 61,500 units
Year	Computation of PV Factor	PV Factor @ 20 %	Cash flow	PV	Cash flow	PV
0	1/(1+0.2)^0	1	($848,000)	($848,000)	($848,000)	($848,000)
1	1/(1+0.2)^1	0.8333333333	$ 429,700	$358,083.33	$ 423,200	$352,666.67
2	1/(1+0.2)^2	0.6944444444	$ 429,700	$298,402.78	$ 423,200	$293,888.89
3	1/(1+0.2)^3	0.5787037037	$ 429,700	$248,668.98	$ 423,200	$244,907.41
4	1/(1+0.2)^4	0.4822530864	$ 429,700	$207,224.15	$ 423,200	$204,089.51
5	1/(1+0.2)^5	0.4018775720	$ 429,700	$172,686.79	$ 423,200	$170,074.59
6	1/(1+0.2)^6	0.3348979767	$ 429,700	$143,905.66	$ 423,200	$141,728.82
7	1/(1+0.2)^7	0.2790816472	$ 429,700	$119,921.38	$ 423,200	$118,107.35
8	1/(1+0.2)^8	0.2325680394	$ 429,700	$99,934.49	$ 423,200	$98,422.79
			NPV	$800,827.57	NPV	$775,886.03

Change in NPV = Base case NPV for sales of 62,000 units – NPV for sales of 61,500 units

                          = $ 800,827.57 - $ 775,886.03 = $ 24,941.54

NPV will decrease by $ 24,941.54

c.

Δ OCF/ Δ VC = ($ 429,700 - $ 423,200)/ ($ 1,240,000 - $ 1,230,000)

                       = $ 6,500/$ 10,000 = 0.65 or 1