Question

A small company purchased now for $23,000 will lose $1,200 each year the first four years. An additional $8,000 invested in the company during the fourth year will result in a profit of $5,500 each year from the fifth year through the fifteenth year. At the end of 15 years, the company can be sold for $33,000.

a. Determine the IRR.
b. Calculate the FW if MARR = 12%.
c. Calculate the ERR when externeal reinvestment rate per period is 12%.

Answer 1

a) The IRR is 10%

b) The FW if MARR = 12% is -$27070.25.

c) The ERR when externeal reinvestment rate per period is 12%. is 10.74%.

Step-by-step explanation:

a)

PW(i%) = -23000 - 1200(P/A, i%, 4) - 8000(P/F, i%, 4) + 5500(P/A, i%, 11)(P/F, i%, 4) + 33000(P/F, i%, 15)

= 0

Solve for i%

IRR = 10%

Therefore, The IRR is 10%

b)

FW (12%) = -23000(F/P, 12%, 15) - 1200(F/A, 12%, 4)(F/P, 12%, 11) - 8000 (F/P, 12%, 11) + 5500(F/A, 12%, 11) + 33000

= -23000(5.4736) - 1200(4.7793)(3.4785) - 8000(3.4785) + 5500(20.6546) + 33000

= -27070.25

Therefore, The FW if MARR = 12% is -$27070.25.

c)

[23000 + 1200(P/A, 12%, 4) + 8800(P/F, 12%, 4)](F/P, i%, 15) = 5500 (F/A, 12%, 11) + 33000

[23000 + 1200(3.0373) + 8000(.6355)](F/P, i%, 15) = 5500(20.6546) + 3300

31725.76 (1 + i)^15 = 146600.3

ERR = 10.74%

Therefore, The ERR when externeal reinvestment rate per period is 12%. is 10.74%.