In: Finance
Consider a project with a 5-year life. The initial cost to set up the project is $100,000. This amount is to be linearly depreciated to zero over the life of the project and there is no salvage value. The required return is 13% and the tax rate is 34%. You've collected the following estimates: Base case Pessimistic Optimistic Unit sales per year (Q) 8,000 6,000 10,000 Price per unit (P) 50 40 60 Variable cost per unit (VC) 20 35 15 Fixed costs per year (FC) 30,000 50,000 20,000
Attempt 3/5 for 10 pts. Part 1 What is the annual free cash flow in the base case?
Attempt 1/5 for 10 pts. Part 2 What is the NPV in the base case?
Attempt 1/5 for 10 pts. Part 3 What is the NPV in the pessimistic case?
Attempt 2/5 for 10 pts. Part 4 What is the NPV in the optimistic case?
Consider a project with a 6-year life. The initial cost to set up the project is $100,000. This amount is to be linearly depreciated to zero over the life of the project and there is no salvage value. The required return is 11% and the tax rate is 34%.
The price per unit is $50, variable costs are $20 per unit and fixed costs are $30,000 per year. You've collected the following estimates for unit sales:
Base case | Pessimistic | Optimistic | |
Unit sales per year (Q) | 7,000 | 5,000 | 9,000 |
Attempt 2/5 for 8 pts.
Part 1
What is the NPV in the base case?
Attempt 1/5 for 10 pts.
Part 2
What is the NPV in the pessimistic case?
Attempt 1/5 for 10 pts.
Part 3
What is the NPV in the optimistic case?
BASE CASE CASH FLOW | ||||||
Initial Cash Flow: | ||||||
Cost of machine | $100,000 | |||||
Annual Cash Flow:(Base Case) | ||||||
a | Sales Quantity | 8000 | ||||
b | Price per unit | $50 | ||||
c=a*b | Sales Revenue | $400,000 | ||||
d | Variable cost per unit | $20 | ||||
e=a*d | AnnualVariable cost | $160,000 | ||||
f | Fixed costs per year | $30,000 | ||||
g | Depreciation expenses | $20,000 | (100000/5) | |||
h=c-e-f-g | Profit before tax | $190,000 | ||||
i=h*34% | Tax expense | $64,600 | ||||
j=h-i | After tax profit | $125,400 | ||||
g | Add: Depreciation (non cash expense) | $20,000 | ||||
k=j+g | Annual Cash Flow: | $145,400 | ||||
Annual Cash Flow in base case | $145,400 | |||||
Part2: NPV of Base Case | ||||||
Present Value (PV)of Cash Flow | ||||||
(Cash Flow)*((1+i)^N) | ||||||
i=Discount rate=Required return =13%= | 0.13 | |||||
N=Year of cash flow | ||||||
N | CF | PV=CF/(1.13^N) | ||||
Year | Cash Flow | Present Value | ||||
0 | ($100,000) | ($100,000) | ||||
1 | $145,400 | $128,672.57 | ||||
2 | $145,400 | $113,869.53 | ||||
3 | $145,400 | $100,769.49 | ||||
4 | $145,400 | $89,176.54 | ||||
5 | $145,400 | $78,917.29 | ||||
Net Present Value=Sum of PV of cash flows | $78,917.29 | |||||
Part 3 NPV of Pessimistic Case | ||||||
Annual Cash Flow:(Pessimistic Case) | ||||||
a | Sales Quantity | 6000 | ||||
b | Price per unit | $40 | ||||
c=a*b | Sales Revenue | $240,000 | ||||
d | Variable cost per unit | $35 | ||||
e=a*d | AnnualVariable cost | $210,000 | ||||
f | Fixed costs per year | $50,000 | ||||
g | Depreciation expenses | $20,000 | (100000/5) | |||
h=c-e-f-g | Profit before tax | ($40,000) | ||||
i=h*34% | Tax expense | ($13,600) | ||||
j=h-i | After tax profit | ($26,400) | ||||
g | Add: Depreciation (non cash expense) | $20,000 | ||||
k=j+g | Annual Cash Flow: | ($6,400) | ||||
Annual Cash Flow in Pessimistic case | ($6,400) | |||||
N | CF | PV=CF/(1.13^N) | ||||
Year | Cash Flow | Present Value | ||||
0 | ($100,000) | ($100,000) | ||||
1 | ($6,400) | -$5,663.72 | ||||
2 | ($6,400) | -$5,012.14 | ||||
3 | ($6,400) | -$4,435.52 | ||||
4 | ($6,400) | -$3,925.24 | ||||
5 | ($6,400) | -$3,473.66 | ||||
Net Present Value=Sum of PV of cash flows | -$3,473.66 | |||||
(pessimistic Case) | ||||||
Part 4 NPV of Optimistic Case | ||||||
Annual Cash Flow:(Optimistic Case) | ||||||
a | Sales Quantity | 10000 | ||||
b | Price per unit | $60 | ||||
c=a*b | Sales Revenue | $600,000 | ||||
d | Variable cost per unit | $15 | ||||
e=a*d | AnnualVariable cost | $150,000 | ||||
f | Fixed costs per year | $20,000 | ||||
g | Depreciation expenses | $20,000 | (100000/5) | |||
h=c-e-f-g | Profit before tax | $410,000 | ||||
i=h*34% | Tax expense | $139,400 | ||||
j=h-i | After tax profit | $270,600 | ||||
g | Add: Depreciation (non cash expense) | $20,000 | ||||
k=j+g | Annual Cash Flow: | $290,600 | ||||
Annual Cash Flow in Optimistic case | $290,600 | |||||
N | CF | PV=CF/(1.13^N) | ||||
Year | Cash Flow | Present Value | ||||
0 | ($100,000) | ($100,000) | ||||
1 | $290,600 | $257,168.14 | ||||
2 | $290,600 | $227,582.43 | ||||
3 | $290,600 | $201,400.38 | ||||
4 | $290,600 | $178,230.42 | ||||
5 | $290,600 | $157,726.04 | ||||
Net Present Value=Sum of PV of cash flows | $157,726.04 | |||||
(Optimistic Case) | ||||||