Answer:
The two IRRs are: - 76.49% and 36.79%
Explanation:
To simplify our "Hard work", let's denote the cash flow numbers in terms of '000 (To reduce the number of zeros).
IRR is that discount rate R, for which NPV = 0
NPV is the sum of discounted cash inflows and outflows. Therefore,
NPV ($'000) = - 39,800 + (63,800 / (1 + R) - [12,800 / (1 + R)2]
When NPV = 0 [If R is the IRR],
0 = - 39,800 + [(63,800 / (1 + R)] - [12,800 / (1 + R)2]
[12,800 / (1 + R)2] - [(63,800 / (1 + R)] + 39,800 = 0
To simplify further, let's put N = 1 + R. Also, let's divide both sides by 200 [Note: We're only doing arithmetical simplification to reduce the large numbers]]:
[64 / (N)2] - (319 / N) + 199 = 0
Multiplying all terms by (N2):
64 - 319N + 199 (N)2 = 0
that is,
199 (N)2 - 319N + 64 = 0
This is a quadratic equation with large coefficients. Solving quadratic equation is outside scope of this question (it belongs to Algebra), so I've used an Online Quadratic equation solver**, which returns following values of N:
N = 1.3679, and N = 0.2351
So:
1 + R = 1.3679, Or 1 + R = 0.2351
R = (1.3679 - 1) or R = (0.2351 - 1)
R = 0.3679 or R = - 0.7649
The two IRRs are: - 76.49% and 36.79%
