Question

****Please calculate the NPV in the table - NOTE the wrong answers I have already submitted in the table. Please then calculate the sensitivity in B. Note my incorrect answer I have already submitted. Thanks!

You are considering a new product launch. The project will cost $2,300,000, have a 4-year life, and have no salvage value; depreciation is straight-line to 0. Sales are projected at 160 units per year; price per unit will be $30,000; variable cost per unit will be $18,500; and fixed costs will be $610,000 per year. The required return on the project is 15%, and the relevant tax rate is 36%.

a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10%. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round the final NPV answers to 2 decimal places. Omit $ sign in your response.)

Scenario	Unit Sales	Variable Cost	Fixed Costs	NPV
Base	160 Correct	$ 18,500 Correct	$ 610,000 Correct	$ 1,248,051.25 Incorrect
Best	176 Correct	$ 16,650 Correct	$ 549,000 Correct	$ 1,807,600.12 Incorrect
Worst	144 Correct	$ 20,350 Correct	$ 671,000 Correct	$ 688,448.60 Incorrect

b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round the final answer to 3 decimal places. Omit $ sign in your response.)

ΔNPV/ΔFC           $ -2.284 Incorrect

****Please calculate the NPV in the table - NOTE the wrong answers I have already submitted in the table. Please then calculate the sensitivity in B. Note my incorrect answer I have already submitted. Thanks!

Answer 1

A. (i) BASE NPV: Sales Less Variable Cost 30000-18500= $11500*160 units= $1840000

Less: Fixed Cost (excl. Depreciation) = ($610000)

Less: Depreciation Exp. = ($575000)

Profit Before tax = $655000

Less Tax @36% = (235800)

Profit after taxes = $419200

Add: Depreciation = $575000

Cash Flow from operations = $994200

Year	Cash Flow	Rate of Return	PV Factor for 4 years	PV amount
1-4	994200	15%	2.85498	2838419.48
Outflow at the year 0				(2300000)
NPV				538419.49

(ii) BEST CASE NPV: Sales Less Variable Cost 30000-16650= $13350*176 units= $2349600

Less: Fixed Cost (excl. Depreciation) = ($549000)

Less: Depreciation Exp. = ($575000)

Profit Before tax = $1225600

Less Tax @36% = (441216)

Profit after taxes = $784384

Add: Depreciation = $575000

Cash Flow from operations = $1359384

Year	Cash Flow	Rate of Return	PV Factor for 4 years	PV amount
1-4	1359384	15%	2.85498	3881011.91
Outflow at the year 0				(2300000)
NPV				1581011.91

(iii) WORST CASE NPV: Sales Less Variable Cost 30000-20350= $9650*144 units= $1389600

Less: Fixed Cost (excl. Depreciation) = ($671000)

Less: Depreciation Exp. = ($575000)

Profit Before tax = $143600

Less Tax @36% = ($51696)

Profit after taxes = $91904

Add: Depreciation = $575000

Cash Flow from operations = $666904

Year	Cash Flow	Rate of Return	PV Factor for 4 years	PV amount
1-4	666904	15%	2.85498	1903996.49
Outflow at the year 0				(2300000)
NPV				(396003.51)

B. Sensitivity of BASE NPV to the changes in Fixed Costs:

Sales Less Variable Cost 30000-18500= $11500*160 units= $1840000

Less: Fixed Cost (excl. Depreciation) = ($671000)

Less: Depreciation Exp. = ($575000)

Profit Before tax = $594000

Less Tax @36% = (213840)

Profit after taxes = $380160

Add: Depreciation = $575000

Cash Flow from operations = $955160

Year	Cash Flow	Rate of Return	PV Factor for 4 years	PV amount
1-4	955160	15%	2.85498	2726961.13
Outflow at the year 0				(2300000)
NPV				426961.13

% Change in NPV = 426961.13-538419.49/538419.49 = -20.701%

Sensitivity of NPV = -20.701%/10% = -2.070%

This means that with an increase in fixed costs of 1%, the NPV of a project will decrease by 2.070%, and vice versa, if fixed costs are reduced by 1%, the NPV will increase by 2.070%.