Question

1) A small company purchased now for $23,000 will lose $1,200 each year for the first four years. An additional $8,000 is invested in the company during the fourth year will result in a profit of $5,500 each year from the fifth through to fifteen year. At the end of 15 year the company can be sold for $33,000. The desired rate of return is 15%. A) Calculate the NPV of the project.(3 points) B) Determine the IRR?(3 points) C) Calculate the future worth in MARR = 12% (2 points)

Answer #1

Initial Cost = 23,000

Loss = 1,200 per year for the first 4 years

Additional investment = 8,000 at 4^{th} year

Profit = 5,500 per year from 5^{th} to 15^{th}
year (11 years)

Salvage Value = 33,000

Desired Rate of Return = 15%

a. Calculate NPV (rate of interest = 15%)

NPV = -23,000 – 1,200 (P/A, 15%, 4) – 8,000 (P/F, 15%, 4) + 5,500 (P/A, 15%, 11) (P/F, 15%, 4) + 33,000 (P/F, 15%, 15)

NPV = -23,000 – 1,200 (2.85498) – 8,000 (0.57175) + 5,500 (5.23371) (0.57175) + 33,000 (0.12289)

**NPV = -10,486.55**

b. Calculate IRR

Calculating IRR using Trial & Error Method

Let the rate of interest is 10%. Calculate the PW at 10%.

NPV = -23,000 – 1,200 (P/A, 10%, 4) – 8,000 (P/F, 10%, 4) + 5,500 (P/A, 10%, 11) (P/F, 10%, 4) + 33,000 (P/F, 10%, 15)

NPV = -23,000 – 1,200 (3.16987) – 8,000 (0.68301) + 5,500 (6.49506) (0.68301) + 33,000 (0.23939)

NPV = 31

The NPV is positive. Increase the rate of interest to get negative PW. Increase the rate of interest to 11% and calculate the NPV.

NPV = -23,000 – 1,200 (P/A, 11%, 4) – 8,000 (P/F, 11%, 4) + 5,500 (P/A, 11%, 11) (P/F, 11%, 4) + 33,000 (P/F, 11%, 15)

NPV = -23,000 – 1,200 (3.10245) – 8,000 (0.65873) + 5,500 (6.20652) (0.65873) + 33,000 (0.20900)

NPV = -2,609

Using Interpolation

**IRR = 10% + [31 – 0 ÷ 31 – (-2,609)] * 1% = 10.01 or
10%**

c. Calculate FW at 12%

FW = -23,000 (F/P, 12%, 15) – 1,200 (F/A, 12%, 4) (F/P, 12%, 11) – 8,000 (F/P, 12%, 11) + 5,500 (F/A, 12%, 11) + 33,000

FW = -23,000 (5.4736) – 1,200 (4.7793) (3.4785) – 8,000 (3.4785) + 5,500 (20.6546) + 33,000

**FW = -27,070.25**

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