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A company is considering an investment project that would cost $8 million today and yield a payoff of $10 million in 5 years.
Complete the following table by indicating whether the firm should undertake the project for each of the interest rates listed.
Undertake Project?
Yes No
Interest Rate
7%
6%
оооо
5%
4%

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Answer:

Kindly see explanation

Explanation:

Given the following:

Initial investment = $8,000,000

Future value (FV) = $10,000,000

PERIOD (t) = 5 Years

To know if the form should undertake the project, the present value(PV) at each interest rate should be calculated ;

A.) Interest rate (r) = 7% = 0.07

PV = FV / (1 + r)^t

PV = 10,000,000 / (1 + 0.07)^5

PV = 10,000,000 / 1.07^5

PV = 10,000,000 / 1.4025517307

PV = $7,129,861.79483668

Should not be undertaken, PV is less than initial investment.

B.) Interest rate (r) = 6% = 0.06

PV = FV / (1 + r)^t

PV = 10,000,000 / (1 + 0.06)^5

PV = 10,000,000 / 1.06^5

PV = 10,000,000 / 1.3382255776

PV = $7,472,581.72866057

Should not be undertaken, PV is less than initial investment.

C.) Interest rate (r) = 5% = 0.05

PV = FV / (1 + r)^t

PV = 10,000,000 / (1 + 0.05)^5

PV = 10,000,000 / 1.05^5

PV = 10,000,000 / 1.2762815625

PV = $7,835,261.66468459

Should not be undertaken, PV is less than initial investment

D.)Interest rate (r) = 4% = 0.04

PV = FV / (1 + r)^t

PV = 10,000,000 / (1 + 0.04)^5

PV = 10,000,000 / 1.04^5

PV = 10,000,000 / 1.2166529024

PV = $8,219,271.06759351

Should be undertaken, PV is greater than initial investment

The firm should undertake the project for each of the interest rates listed for Undertake Project :

A) 7% is No.

B) 6% is No.

C) 5% is No.

D) 4% is Yes.

Undertake Project

Given:

Initial investment = $8,000,000

Future value (FV) = $10,000,000

PERIOD (t) = 5 Years

Part A:

Initial investment = $8,000,000

Future value (FV) = $10,000,000

Time (t) = 5 Years

Interest rate (r) = 7% = 0.07

Present Value =PV[tex]PV = FV / (1 + r)^t[/tex]

PV =[tex]10,000,000 / (1 + 0.07)^5PV = 10,000,000 / 1.07^5[/tex]

PV = [tex]10,000,000 / 1.4025517307[/tex]

PV = [tex]$7,129,861.79483668.[/tex]

Thus, the project should not be undertaken as the present value is less than initial investment.

Part B:

Initial investment = $8,000,000

Future value (FV) = $10,000,000

Time (t) = 5 Years

Present Value =PV

Interest rate (r) = 6% = 0.06[tex]

PV = FV / (1 + r)^t[/tex]

PV = [tex]10,000,000 / (1 + 0.06)^5[/tex]

PV =[tex]10,000,000 / 1.06^5[/tex]

PV = [tex]10,000,000 / 1.3382255776[/tex]

PV = [tex]$7,472,581.72866057[/tex]

Thus, the project should not be undertaken as the Present value is less than initial investment.

Part C:

Initial investment = $8,000,000

Future value (FV) = $10,000,000

Time (t) = 5 Years

Present Value =PV

Interest rate (r) = 5% = 0.05[tex]

PV = FV / (1 + r)^t[/tex]

PV =[tex]10,000,000 / (1 + 0.05)^5[/tex]

PV =[tex]10,000,000 / 1.05^5[/tex]

PV = [tex]$7,835,261.66468459[/tex]

Thus, the project should not be undertaken as the Present value is less than initial investment.

Part D:

Initial investment = $8,000,000

Future value (FV) = $10,000,000

Time (t) = 5 Years

Present Value =PV

Interest rate (r) = 4% = 0.04

PV = FV / (1 + r)^t[/tex]

PV = [tex]10,000,000 / (1 + 0.04)^5[/tex]

PV = [tex]10,000,000 / 1.04^5[/tex]

PV = [tex]10,000,000 / 1.2166529024[/tex]

PV = [tex]$8,219,271.06759351[/tex]

Thus, the project should be undertaken as the Present Value is greater than initial investment.

Thus, the correct option is D.

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