Question

A firm is considering a simple investment project. If it goes forward, then the firm must pay $900 now, but it receives a payment of $400 in each of the following three years. Except as noted, each part of the problem is worth 5 points.(a) [16 points] You should calculate, to the nearest dollar, the present value of this project for four different scenarios. Assume that the firm’s opportunity cost of capital is simply the (risk-adjusted) market interest rate. Scenario A: The interest rate is 14%. Scenario B: The interest rate is 17%. For the second two scenarios, assume that the OCC is 20%, but there is also inflation. The effect of inflation is to increase the value of the payment received by the inflation rate, with each year that passes. The payment that would have been $400 initially exceeds $400 by the time it occurs a year later, and each year’s payment will be larger than the previous year’s payment. Scenario C: The inflation rate is 2%. Scenario D: The inflation rate is 5%.(b) In which scenarios is the project profitable? (You should briefly justify your answers.)(c) Can you find two scenarios such that the scenario with the higher interest rate also produces less investment? Can you find two scenarios such that the scenario with the higher interest rate also produces more investment?

Answer 1

Answer:

a) scenario A NPV positive 28.68, scenario B NPV Negative 16.16, scenario C NPV positive 664.92, scenario D NPV positive 889.72 (b) The scenario with the highest positive NPV is the most profitable (c) The scenario B with the interest rate of 17% has Negative NPV of 16.16 produces less investment (d) The scenario C with the highest interest rate of 20% has the positive NPV of 664.92 he scenario D with the highest interest rate of 20% has the highest positive NPV of 889.72, produces more investment

Explanation:

Calculation of Discount Factor

Effective rate for scenario C and D

Using the formula (1 + m/1 + i)∧n - 1 Where i = rate of inflation, m = cost of capital, n = numbers of years

For C since interest rate = 20% = 20÷100 = 0.2, since rate of inflation = 2% = 2÷100 = 0.02

(1 + 0.2/1 + 0.02)∧n - 1

= 1.2 /1.02 -1

=1.1764 -1

=0.1764 ×100 = 17.64%

Discount Factor for C using the formula ( 1 + r)∧-n -1/ r since n = 3 ,r = 0.1764

= ( 1 + 0.2)∧-3 - 1/ 0.1764

= (1.2)∧-3 -1/0.1764

=0.5787 -1

= 0.4213÷ 0.1764

= 2.3883

For D Effective rate

( 1 + 0.2)∧n - 1/(1 + 0.05)

= 1.2/1.05 -1

=1.1428 -1

= 0.1428 × 100 = 14.28%

DF for D

= (1 + 0.2)∧-3 -1 / 0.1428

=0.5787 -1 = 0.4213

=0.4213÷0.1428

=2.9503

DF for year 1 and 2 for C and D

Using the formula ( 1 + r) ∧-n

( 1 + 0.2)∧-1 = ( 1.2)∧-1 = 0.83

(1 + 0.2)∧-2 = (1.2)∧-2 = 0.694

DF for scenario A For year 1 -3 using ( 1+ r)∧-n

= ( 1 + 0.14)∧-1 = (1.14)∧-1 = 0.8772

= (1+0.14)∧-2 = (1.14)∧-2 = 0.7695

=(1+0.14)∧-3 = (1.14)∧-3 = 0.6750

DF for scenario B using the same formula

=( 1 + 0.17)∧-1 =(1.17)∧-1 = 0.8547

=(1+0.17)∧-2 = (1.17)∧-2 = 0.7305

=(1 + 0.17)∧-3 = (1.17)∧-3 = 0.6244

Scenario A

Year. C.F. DF PV

$ $

0. 900 1 (900)

1 400 0.8772 350.88

2 400 0.7695 307.8

3 400 0.6750 270

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NPV positive 28.68

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Workings = C F × DF = PV

Scenario B

Year. CF DF PV

$ $

0 900 1 (900)

1. 400 0.8547 341.88

2 400 0.7305 292.2

3. 400 0.6244 249.76

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NPV Negative 16.16

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Scenario C

Year CF DF PV

$ $

0 900 1 (900)

1 400 0.83 332

2 400 0.694 277.6

1-3 400 2.3883. 955.32

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NPV positive 664.92

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Scenario D

Year CF DF PV

$ $

0 900 1 (900)

1 400 0.83 332

2. 400 0.694 277.6

1-3 400 2.9503 1,180.12

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NPV positive 889.72

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