Question
Needing help with portion b-3 and c. I have solved the other portions. We are evaluating...
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 $
Answers
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