Question

Suppose Mr. Agirich has decided to buy a center pivot irrigation system but can't decide between buying a new or used system. Mr. Agirich has determined that the NPV(new)=$4,500 and the NPV(used)=$2,000. Mr. Agirich wants to choose the new system because it has a higher NPV but is not sure because he has heard that NPV is not the correct criterion for investment comparisons if the investments have different economic lives. Suppose Mr. Agirich learns that you have taken a financial management course at TAMU and has asked you to help him decide whether to buy the new or used irrigation system.

He provides the additional information: Mr. Agirich requires at least a 15% pre-tax rate of return on investments, the marginal tax rate is 40%, the expected rate of inflation is 3.8%, the economic life of the new system is 15 years and the economic life of the used system is 5 years. Should Mr. Agirich buy the new or used irrigation system?

What is the nominal pre-tax discount rate?

A. 15%

B. 9%

C. 5%

D. 3.8%

E. None of the above

What is the nominal after-tax discount rate?

A. 15%

B. 9%

C. 5%

D. 3.8%

E. None of the above

What is the real after-tax discount rate?

A. 15%

B. 9%

C. 5%

D. 3.8%

E. None of the above

What is the nominal annuity equivalent for cost of the New System?

A. $461.9

B. $558.3

C. $514.2

D. $433.5

E. None of the above

What is the real annuity equivalent for cost of the New System?

A. $461.9

B. $558.3

C. $514.2

D. $433.5

E. None of the above

What is the nominal annuity equivalent for cost of the Used System?

A. $461.9

B. $558.3

C. $514.2

D. $433.5

E. None of the above

What is the real annuity equivalent for cost of the Used System?

A. $461.9

B. $558.3

C. $514.2

D. $433.5

E. None of the above

The annualized cost is less for the New System?

A. True

B. False

Answer 1

1)

Nominal pre tax discount rate = 15% (already given in question)

2)

Nominal after tax discount rate = 15%*(1 - tax)

= 15%*(1-0.4)

=9%

3)

after tax real rate = [(1+after tax nominal) / (1+inflation rate)] - 1

= [(1+9%) / (1+3.8%)] - 1

= 5%

4)

PVIFA(n = 15 ; r = 9%) = 8.060688

annuity equivalent = 4500 / 8.060688 = $558.3

(formula for PVIFA = [ 1 - (1+r)^-n / r ]

5)

PVIFA(n = 15 ; r = 5%) = 10.37966

annuity equivalent = 4500 / 10.37966 = $433.5

6)

PVIFA(n = 5 ; r = 9%) = 3.88965

annuity equivalent = 2,000 / 3.88965 = $514.2

7)

PVIFA(n = 5 ; r = 5%) = 4.329477

annuity equivalent = 2,000 / 4.329477 = $461.9

8)

False , annualized cost is less for used system