Question

The technique for calculating a bid price can be extended to many other types of problems. Answer the following questions using the same technique as setting a bid price; that is, set the project NPV to zero and solve for the variable in question. Guthrie Enterprises needs someone to supply it with 152,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost $1,920,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that in five years this equipment can be salvaged for $162,000. Your fixed production costs will be $277,000 per year, and your variable production costs should be $10.60 per carton. You also need an initial investment in net working capital of $142,000. The tax rate is 22 percent and you require a return of 12 percent on your investment. Assume that the price per carton is $17.20.

  

a.	Calculate the project NPV. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.	What is the minimum number of cartons per year that can be supplied and still break even? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

c.	What is the highest fixed costs that could be incurred and still break even? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a) Statement showing NPV

Particulars	0	1	2	3	4	5	NPV = Sum of PV
Cost of equipment	-1920000
WC Required	-142000
Selling price per unit		17.2	17.2	17.2	17.2	17.2
Less : Variable cost per unit	10.6	10.6	10.6	10.6	10.6
Contribution per unit		6.6	6.6	6.6	6.6	6.6
No of units to be sold		152000	152000	152000	152000	152000
Total contribution		1003200	1003200	1003200	1003200	1003200
Fixed cost		-277000	-277000	-277000	-277000	-277000
Depreciation		-384000	-384000	-384000	-384000	-384000
PBT		342200	342200	342200	342200	342200
Tax @ 22%		75284	75284	75284	75284	75284
PAT		266916	266916	266916	266916	266916
Add : Depreciation		384000	384000	384000	384000	384000
Annual cash flow		650916	650916	650916	650916	650916
Release of WC						142000
Salvage value of Machine =162000 (1-tax rate) =162000(1-0.22) = 162000(0.78) =126360						126360
Total cash flow	-2062000	650916	650916	650916	650916	919276
PVIF @ 12%	1.0000	0.8929	0.7972	0.7118	0.6355	0.5674
PV	-2062000.00	581175.00	518906.25	463309.15	413668.89	521621.89	436681.18

Thus NPV = 436681.18 $

b) Break even point is whine NPV = 0

Thus,

Initial Investment = Annual cash flow x PVIFA(12%,5) + Terminal value x PVIF(12%,5)

Now we now that Initial cash flow = 2062000 $

Termianl cash flow = Release of WC + Salavage value of machine

= 142000 + 126360

= $268360

PVIFA(12%,5) = 3.6048 ( Sum of all PVIF)

PVIF(12%5) = 0.5674

Thus

2062000 = Annual cash flow x 3.6048 + 268360 x 0.5674

2062000 =  Annual cash flow x 3.6048 + 152274.67

1909725.33 = Annual cash flow x 3.6048

Annual cash flow = 529772.89 $

Annual cash flow = PAT + Depreciation

Depreciation = 384000

Thus 529772.89 = PAT + 384000

PAT = 145772.89

now PAT = PBT(1-tax rate)

=145772.89 = PBT(1-0.22)

PBT = 145772.89/0.78

PBT = 186888.33$

Now Total contribution - Fixed cost - depreciaton = PBT

Thus 186888.33 = Total contribution - 277000 - 384000

Total contribution = 186888.33 + 277000+384000

Total contribution = 847888.33 $

Now Contribution per unit = 6.6$

Thus no of units required to breakeven = 847888.33 /6.6

=128467.93 units

i.e 128468 units

c) Here we need to find highest fixed cost till financial break even

Thus

Initial Investment = Annual cash flow x PVIFA(12%,5) + Terminal value x PVIF(12%,5)

2062000 = Annual cash flow x 3.6048 + 268360 x 0.5674

2062000 =  Annual cash flow x 3.6048 + 152274.67

1909725.33 = Annual cash flow x 3.6048

Annual cash flow = 529772.89 $

Annual cash flow = PAT + Depreciation

Depreciation = 384000

Thus 529772.89 = PAT + 384000

PAT = 145772.89

now PAT = PBT(1-tax rate)

=145772.89 = PBT(1-0.22)

PBT = 145772.89/0.78

PBT = 186888.33$

Now Total contribution - Fixed cost - depreciaton = PBT

Total contribution = 1003200 $ ( 152000 units x 6.6$)

Thus 10032000 - Fixed cost - 384000 = 186888.33

619200 - Fixed cost = 186888.33

Thus Fixed cost = 432311.67 $