Corner Jewelers, Inc. recently analyzed the project whose cash flows are shown below. However, before the company decided to accept or reject the project, the Federal Reserve changed interest rates and therefore the firm's cost of capital (r). The Fed's action did not affect the forecasted cash flows. By how much did the change in the r affect the project's forecasted NPV? Note that a project's expected NPV can be negative, in which case it should be rejected.Old r: 8.00% New r: 11.25%Year 0 1 2 3Cash flows −$1,000 $410 $410 $410a. −$59.03b. −$56.08c. −$53.27d. −$50.61e. −$48.08

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-11-05T09:50:38+01:00

Answer:

correct option is a. −$59.03

Explanation:

given data

Old cost of capital (r) 8.00% New cost of capital (r) 11.25%

year 0 1 2 3

cash flow -$1000 $410 $410 $410

solution

we know that here old cost of capital (r) NPV will be

old cost of capital (r) NPV = cash flow 0 year + cash flow × [tex]\frac{1-(1+rate)^{-time}}{rate}[/tex]

put here value

old cost of capital (r) NPV = -1000 + 410 × [tex]\frac{1-(1+0.08)^{-3}}{0.08}[/tex]

old cost of capital (r) NPV = $56.61

and

new cost of capital (r) NPV will be

new cost of capital (r) NPV = cash flow 0 year + cash flow × [tex]\frac{1-(1+rate)^{-time}}{rate}[/tex]

put here value

new cost of capital (r) NPV = -1000 + 410 × [tex]\frac{1-(1+0.1125)^{-3}}{0.1125}[/tex]

new cost of capital (r) NPV = -$2.42

so difference is

Difference = -$2.42 - $56.61

Difference = -$59.03

so correct option is a. −$59.03