Question
In: Finance
The technique for calculating a bid price can be extended to many other types of problems....
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 129,000 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 you $960,000 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 $79,000. Your fixed production costs will be
$334,000 per year, and your variable production costs should be
$11.20 per carton. You also need an initial investment in net
working capital of $84,000. Assume the tax rate is 35 percent and
the required return on the investment is 12 percent.
a. Assuming that the price per carton is $17.90,
what is the NPV of this project? (Do not round intermediate
calculations and round your answer to 2 decimal places, e.g.,
32.16.)
NPV $
b. Assuming that the price per carton is $17.90,
find the quantity of cartons per year you need to supply to break
even. (Do not round intermediate calculations and round
your answer to nearest whole number.)
Quantity of cartons
c. Assuming that the price per carton is $17.90,
find the highest level of fixed costs you could afford each year
and still break even. (Do not round intermediate
calculations and round your answer to 2 decimal places, e.g.,
32.16.)
Fixed costs
$
Solutions
Expert Solution
(a)
| Calculation of NPV | |||
| Year | Cashflow | DF @12% | PV |
| 0 | $ (1,044,000) | 1.0000 | $ (1,044,000.00) |
| 1 | $ 411,895 | 0.8929 | $ 367,763.39 |
| 2 | $ 411,895 | 0.7972 | $ 328,360.17 |
| 3 | $ 411,895 | 0.7118 | $ 293,178.73 |
| 4 | $ 411,895 | 0.6355 | $ 261,766.72 |
| 5 | $ 547,245 | 0.5674 | $ 310,521.51 |
| Net Present Value | $ 517,590.52 |
| Calculation of Cashflow | ||||||
| Particular | Year-0 | Year-1 | Year-2 | Year-3 | Year-4 | Year-5 |
| Sell Price | - | $ 17.90 | $ 17.90 | $ 17.90 | $ 17.90 | $ 17.90 |
| Less : Variable Cost | - | $ 11.20 | $ 11.20 | $ 11.20 | $ 11.20 | $ 11.20 |
| Contribution | - | $ 6.70 | $ 6.70 | $ 6.70 | $ 6.70 | $ 6.70 |
| Cartons (Supply to Company) | - | 129000 | 129000 | 129000 | 129000 | 129000 |
| Total Contribution | - | $ 864,300 | $ 864,300 | $ 864,300 | $ 864,300 | $ 864,300 |
| Less : Fixed Cost | - | $ 334,000 | $ 334,000 | $ 334,000 | $ 334,000 | $ 334,000 |
| Less : Depreciation | - | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 |
| Earning before Tax | - | $ 338,300 | $ 338,300 | $ 338,300 | $ 338,300 | $ 338,300 |
| Tax @ 35% | - | $ 118,405 | $ 118,405 | $ 118,405 | $ 118,405 | $ 118,405 |
| Earning after Tax | - | $ 219,895 | $ 219,895 | $ 219,895 | $ 219,895 | $ 219,895 |
| Add : Depreciation | - | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 |
| Inflow after tax | - | $ 411,895 | $ 411,895 | $ 411,895 | $ 411,895 | $ 411,895 |
| Less : Equipment Cost | $ 960,000 | - | - | - | - | - |
| Less : Increase in Working Capital | $ 84,000 | - | - | - | - | - |
| Add : Release of Working Capital | - | - | - | - | - | $ 84,000 |
| Add : Salvage Value | - | - | - | - | - | $ 51,350 |
| Net Cashflow | $ (1,044,000) | $ 411,895 | $ 411,895 | $ 411,895 | $ 411,895 | $ 547,245 |
| Calculation of depreciation | |
| Particular | Amount |
| Equipment cost | $ 960,000 |
| Life of Equipment | 5 Years |
| Depreciation | $ 192,000 |
| Salvage Value | |
| Particular | Amount |
| Selling Price | $ 79,000 |
| Less : Book Value | $ - |
| Capital Gain | $ 79,000 |
| Tax @ 35% | $ 27,650 |
| Selling Price | $ 79,000 |
| Less : Tax | $ 27,650 |
| Net Cashflow | $ 51,350 |
(b)
We assume cartons 'x' supply to company so that NPV = 0
| Calculation of NPV | |||
| Year | Cashflow | DF @12% | PV |
| 0 | $ (1,044,000) | 1.0000 | $ (1,044,000.00) |
| 1 | $4.355x - $149,900 | 0.8929 | $3.8884x - $133,845.71 |
| 2 | $4.355x - $149,900 | 0.7972 | $3.4718x - $119,499.36 |
| 3 | $4.355x - $149,900 | 0.7118 | $3.0998x - $106,695.86 |
| 4 | $4.355x - $149,900 | 0.6355 | $2.7677x - $95,264.16 |
| 5 | $4.355x - $14,550 | 0.5674 | $2.4711x-$8,256.06 |
| Net Present Value | $15.6988x - $1,507,561.15 |
| Calculation of Cashflow | ||||||
| Particular | Year-0 | Year-1 | Year-2 | Year-3 | Year-4 | Year-5 |
| Sell Price | - | $ 17.90 | $ 17.90 | $ 17.90 | $ 17.90 | $ 17.90 |
| Less : Variable Cost | - | $ 11.20 | $ 11.20 | $ 11.20 | $ 11.20 | $ 11.20 |
| Contribution | - | $ 6.70 | $ 6.70 | $ 6.70 | $ 6.70 | $ 6.70 |
| Cartons (Supply to Company) | - | x | x | x | x | x |
| Total Contribution | - | $6.70x | $6.70x | $6.70x | $6.70x | $6.70x |
| Less : Fixed Cost | - | $ 334,000 | $ 334,000 | $ 334,000 | $ 334,000 | $ 334,000 |
| Less : Depreciation | - | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 |
| Earning before Tax | - | $6.70x - $526,000 | $6.70x - $526,000 | $6.70x - $526,000 | $6.70x - $526,000 | $6.70x - $526,000 |
| Tax @ 35% | - | $2.345x - $184,100 | $2.345x - $184,100 | $2.345x - $184,100 | $2.345x - $184,100 | $2.345x - $184,100 |
| Earning after Tax | - | $4.355x - $341,900 | $4.355x - $341,900 | $4.355x - $341,900 | $4.355x - $341,900 | $4.355x - $341,900 |
| Add : Depreciation | - | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 |
| Inflow after tax | - | $4.355x - $149,900 | $4.355x - $149,900 | $4.355x - $149,900 | $4.355x - $149,900 | $4.355x - $149,900 |
| Less : Equipment Cost | $ 960,000 | - | - | - | - | - |
| Less : Increase in Working Capital | $ 84,000 | - | - | - | - | - |
| Add : Release of Working Capital | - | - | - | - | - | $ 84,000 |
| Add : Salvage Value | - | - | - | - | - | $ 51,350 |
| Net Cashflow | $ (1,044,000) | $4.355x - $149,900 | $4.355x - $149,900 | $4.355x - $149,900 | $4.355x - $149,900 | $4.355x - $14,550 |
| Calculation of depreciation | |
| Particular | Amount |
| Equipment cost | $ 960,000 |
| Life of Equipment | 5 Years |
| Depreciation | $ 192,000 |
| Salvage Value | |
| Particular | Amount |
| Selling Price | $ 79,000 |
| Less : Book Value | $ - |
| Capital Gain | $ 79,000 |
| Tax @ 35% | $ 27,650 |
| Selling Price | $ 79,000 |
| Less : Tax | $ 27,650 |
| Net Cashflow | $ 51,350 |
as we know B.E.P. means NPV should be zero.
so
$15.6988x - $1,507,561.15 = 0
$15.6988x = $1,507,561.15
x = 96,030.34 or say 96030 cartons should be supply so company can reach B.E.P. of NPV.
(c)
We assume Fixed cost is 'x' so that NPV = 0
| Calculation of NPV | |||
| Year | Cashflow | DF @12% | PV |
| 0 | $ (1,044,000) | 1.0000 | $ (1,044,000.00) |
| 1 | $628,995 - 0.65x | 0.8929 | $561,602.68 - 0.5804x |
| 2 | $628,995 - 0.65x | 0.7972 | $501,430.96 - 0.5182x |
| 3 | $628,995 - 0.65x | 0.7118 | $447,706.22 - 0.4627x |
| 4 | $628,995 - 0.65x | 0.6355 | $399,737.69 - 0.4131x |
| 5 | $764,345 - 0.65x | 0.5674 | $433,709.88 - 0.3688x |
| Net Present Value | $1,300,187.43 - 2.3431x |
| Calculation of Cashflow | ||||||
| Particular | Year-0 | Year-1 | Year-2 | Year-3 | Year-4 | Year-5 |
| Sell Price | - | $ 17.90 | $ 17.90 | $ 17.90 | $ 17.90 | $ 17.90 |
| Less : Variable Cost | - | $ 11.20 | $ 11.20 | $ 11.20 | $ 11.20 | $ 11.20 |
| Contribution | - | $ 6.70 | $ 6.70 | $ 6.70 | $ 6.70 | $ 6.70 |
| Cartons (Supply to Company) | - | 129000 | 129000 | 129000 | 129000 | 129000 |
| Total Contribution | - | $ 864,300 | $ 864,300 | $ 864,300 | $ 864,300 | $ 864,300 |
| Less : Fixed Cost | - | x | x | x | x | x |
| Less : Depreciation | - | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 |
| Earning before Tax | - | $672,300 - x | $672,300 - x | $672,300 - x | $672,300 - x | $672,300 - x |
| Tax @ 35% | - | $235,305 - 0.35x | $235,305 - 0.35x | $235,305 - 0.35x | $235,305 - 0.35x | $235,305 - 0.35x |
| Earning after Tax | - | $436,995 - 0.65x | $436,995 - 0.65x | $436,995 - 0.65x | $436,995 - 0.65x | $436,995 - 0.65x |
| Add : Depreciation | - | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 | $ 192,000 |
| Inflow after tax | - | $628,995 - 0.65x | $628,995 - 0.65x | $628,995 - 0.65x | $628,995 - 0.65x | $628,995 - 0.65x |
| Less : Equipment Cost | $ 960,000 | - | - | - | - | - |
| Less : Increase in Working Capital | $ 84,000 | - | - | - | - | - |
| Add : Release of Working Capital | - | - | - | - | - | $ 84,000 |
| Add : Salvage Value | - | - | - | - | - | $ 51,350 |
| Net Cashflow | $ (1,044,000) | $628,995 - 0.65x | $628,995 - 0.65x | $628,995 - 0.65x | $628,995 - 0.65x | $764,345 - 0.65x |
| Calculation of depreciation | |
| Particular | Amount |
| Equipment cost | $ 960,000 |
| Life of Equipment | 5 Years |
| Depreciation | $ 192,000 |
| Salvage Value | |
| Particular | Amount |
| Selling Price | $ 79,000 |
| Less : Book Value | $ - |
| Capital Gain | $ 79,000 |
| Tax @ 35% | $ 27,650 |
| Selling Price | $ 79,000 |
| Less : Tax | $ 27,650 |
| Net Cashflow | $ 51,350 |
as we know B.E.P. means NPV should be zero.
so
$1,300,187.43 - 2.3431x = 0
2.3431x = $1,300,187.43
x = $554,900.53 or say $554,900
Highest level of Fixed cost is $554,900.53, It could afford each year and still break even.
If any help require help regarding this question please comment, I will help.
jeff jeffy answered 1 year agoRelated Solutions
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many other types of problems. Answer the following questions using
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NPV to zero and solve for the variable in question. Guthrie
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machine screws per year to support its manufacturing needs over the
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many other types of problems. Answer the following questions using
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NPV to zero and solve for the variable in question.
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many other types of problems. Answer the following questions using
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