Concept explainers
a.
Calculate
a.
Explanation of Solution
Calculate NPV of salary received by Mrs. X.
| Year 0 | Year 1 | Year 2 | NPV | |
| Before-tax | $80,000 | $80,000 | $80,000 | |
| Less: Tax cost | $(20,000) | $(32,000) | $(32,000) | |
| After-tax cash flow | $60,000 | $48,000 | $48,000 | |
| Multiply: Discount factor at 8% | - | |||
| Present value | $60,000 | $44,448 | $41,136 | $145,584 |
Working note:
Calculate tax cost.
| Year 1 | Year 2 | Year 3 | |
| Before-tax income | $80,000 | $80,000 | $80,000 |
| Multiply: Marginal tax rate | |||
| Tax cost | $20,000 | $32,000 | $32,000 |
Hence, the NPV of salary received by Mrs. X is $145,584.
Calculate NPV of salary cost to Firm B.
| Year 0 | Year 1 | Year 2 | NPV | |
| Before-tax cash flow | -$80,000 | -$80,000 | -$80,000 | |
| Add: Tax savings | $27,200 | $27,200 | $27,200 | |
| After-tax cash flow | -$52,800 | -$52,800 | -$52,800 | |
| Multiply: Discount factor at 8% | - | |||
| Present value | -$52,800 | -$48,893 | -$45,250 | -$146,943 |
Working note:
Calculate tax savings.
| Year 1 | Year 2 | Year 3 | |
| Before-tax deduction | -$80,000 | -$80,000 | -$80,000 |
| Multiply: Marginal tax rate | |||
| Tax savings | -$27,200 | -$27,200 | -$27,200 |
Hence, the NPV of salary cost to Firm B is -$146,943.
b.
Calculate net present value (NPV) of salary received by Mrs. X and NPV of salary cost to Firm B.
b.
Explanation of Solution
Calculate NPV of salary received by Mrs. X.
| Year 0 | Year 1 | Year 2 | NPV | |
| Before-tax cash flow | $140,000 | $50,000 | $50,000 | |
| Less: Tax cost | $(35,000) | $(20,000) | $(20,000) | |
| After-tax cash flow | $105,000 | $30,000 | $30,000 | |
| Multiply: Discount factor at 8% | - | |||
| Present value | $105,000 | $27,780 | $25,710 | $158,490 |
Working note:
Calculate tax cost.
| Year 1 | Year 2 | Year 3 | |
| Before-tax income | $140,000 | $50,000 | $50,000 |
| Multiply: Marginal tax rate | |||
| Tax cost | $35,000 | $20,000 | $20,000 |
The NPV of salary received by Mrs. X is $158,490.
Calculate NPV of salary cost to Firm B.
| Year 0 | Year 1 | Year 2 | NPV | |
| Before-tax cash flow | -$140,000 | -$50,000 | -$50,000 | |
| Add: Tax savings | $47,600 | $17,000 | $17,000 | |
| After-tax cash flow | -$92,400 | -$33,000 | -$33,000 | |
| Multiply: Discount factor at 8% | - | |||
| Present value | -$92,400 | -$30,558 | -$28,281 | -$151,239 |
Working note:
Calculate tax savings.
| Year 1 | Year 2 | Year 3 | |
| Before-tax deduction | -$140,000 | -$50,000 | -$50,000 |
| Multiply: Marginal tax rate | |||
| Tax savings | -$47,600 | -$17,000 | -$17,000 |
c.
Calculate net present value (NPV) of cost to Firm B under the proposal and state whether the proposal is superior to its original offer.
c.
Explanation of Solution
Calculate NPV of cost to Firm B under the proposal.
| Year 0 | Year 1 | Year 2 | NPV | |
| Before-tax cash flow | -$140,000 | -$45,000 | -$45,000 | |
| Add: Tax savings | $47,600 | $15,300 | $15,300 | |
| After-tax cash flow | -$92,400 | -$29,700 | -$29,700 | |
| Multiply: Discount factor at 8% | - | |||
| Present value | -$92,400 | -$27,502 | -$25,453 | -$145,355 |
Working note:
Calculate tax savings.
| Year 1 | Year 2 | Year 3 | |
| Before-tax deduction | -$140,000 | -$45,000 | -$45,000 |
| Multiply: Marginal tax rate | |||
| Tax savings | -$47,600 | -$15,300 | -$15,300 |
Hence, NPV of cost to Firm B under the proposal is -$145,355.
Comment: The proposal is superior to its original offer as the NVP of salary cost of the proposal (-$145,355) is lower than the NVP of salary cost of the original offer (-$146,943).
d.
State whether Mrs. X should accept the original offer or the counterproposal by calculating net present value (NPV) of salary received.
d.
Explanation of Solution
Calculate NPV of salary received by Mrs. X.
| Year 0 | Year 1 | Year 2 | NPV | |
| Before-tax cash flow | $140,000 | $45,000 | $45,000 | |
| Less: Tax cost | $(35,000) | $(18,000) | $(18,000) | |
| After-tax cash flow | $105,000 | $27,000 | $27,000 | |
| Multiply: Discount factor at 8% | - | |||
| Present value | $105,000 | $25,002 | $23,139 | $153,141 |
Working note:
Calculate tax cost.
| Year 1 | Year 2 | Year 3 | |
| Before-tax income | $140,000 | $45,000 | $45,000 |
| Multiply: Marginal tax rate | |||
| Tax cost | $35,000 | $18,000 | $18,000 |
Comment: Mrs. X should accept the counterproposal as the NPV of salary received of the proposal ($153,141) is higher than the NVP of salary received of the original offer ($145,584).
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Chapter 3 Solutions
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