Question

You have been hired as a capital budgeting analyst by a sporting goods firm that manufactures athletic shoes and has captured 10% of the overall shoe market (the total market is worth $100 million a year). The fixed costs associated with manufacturing these shoes are $2 million a year, and variable costs are 40% of revenues. The company’s tax rate is 40%. The firm believes that it can increase its market share to 20% by investing $10 million in a new distribution system (which can be depreciated over the system’s life of 10 years to a salvage value of zero) and spending $1 million a year in additional advertising. The company proposes to continue to maintain working capital at 10% of annual revenues. The discount rate to be used for this project is 8%.

A.What is the initial investment for this project?

B.What is the annual operating cash flow from this project?

C. What is the NPV of this project?

D. How much would the firm’s market share would have to increase for you to be indifferent to taking or rejecting this project?

Answer 1

Calculation of incremental contribution:

Particular	Before increase	After increase	Incremental
Sale	10000000	20000000	10000000
Variable Cost	4000000	8000000	4000000
Contribution(sale-vc)	6000000	12000000	6000000

Calculation of CFAT:

Partucular	Amount
Contribution	6000000
(-)Depreciation	1000000
(-)Additional Adv.	1000000
Profit before tax	4000000
(-)Tax@40%	1600000
Profit after tax	2400000
(+)Depreciation	1000000
CFAT	3400000

(A) Initial investment=11000000 (i.e. 10000000 in project and 1000000 in working capital)

(B) Annual operating cash flow=3400000

(C) Calculation of NPV:

NPV=PV of CFAT - Initial investment

PV of CFAT=(CFAT*PVAF@8% for 10 years)+(Working capital recovered*PV of $1 receivable after 10 years)

PVAF=[(1+r)^{^n}-1] / [(1+r)^{^n}*r]

=[(1+.08)^{^10}-1] / [(1+.08)^{^10}*.08]

=6.7101

PV of $1 receivable after 10 years=1/(1.08^10)

=.4632

PV of cfat=(6.7101*3400000)+(1000000*.4632)

  =22814340+463200

=23277540

NPV=23277540-11000000

NPV=12277540

(D) Calculation of Desired CFAT for breakeven:

Let the desired CFAT be x

11000000=(6.7101x)+(1000000*.4632)

11000000=6.6101x+463200

6.7101x=10536800

x=1570289.56

Calculation of Desired sale from CFAT (Do back Calculation)

CFAT	1570289.56
(-)Depreciation	1000000
Profit after tax	570289.56
(+)Tax=PAT/60*40	380193.04
PBT	950482.6
(+)Additional Adv	1000000
(+)Depreciation	1000000
Contribution	2950482.6
(+)Variable cost=C/60*40	1966988.4
Incremental Sale	4917471

Incremental market share=4917471/100000000*100

=4.9175%

Hence market share should increase by approx 4.92%