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I had a doubt in the following question's solution:

Problem

Aren't the signs in the equation wrong? Shouldn't it be $-(6,000,000 - 400,000) + 15,000,000(P/F, i^*,15) - 400,000(P/A,i^*,14) = 0$ (using negative signs for cash outflows (disbursements) and positive signs for cash inflows (receipts))? The given solution gives $i^* ≈ 11.6\%$, while, after changing the signs, I get $i^* ≈ 2.57\%$. Which answer is correct?

Leponzo
  • 395

1 Answers1

1

The solution of the picture is correct. You have the Model A (to buy) and Model B (to lease) and the you have to compare the incremental Model B-model A or viceversa. So the cashflows are the following

t       Model A        Model B    Model B-Model A
0   -6,000,000.00   -400,000.00    5,600,000.00 
1                   -400,000.00     -400,000.00 
2                   -400,000.00     -400,000.00 
3                   -400,000.00     -400,000.00 
4                   -400,000.00     -400,000.00 
5                   -400,000.00     -400,000.00 
6                   -400,000.00     -400,000.00 
7                   -400,000.00     -400,000.00 
8                   -400,000.00     -400,000.00 
9                   -400,000.00     -400,000.00 
10                  -400,000.00     -400,000.00 
11                  -400,000.00     -400,000.00 
12                  -400,000.00     -400,000.00 
13                  -400,000.00     -400,000.00 
14                  -400,000.00     -400,000.00 
15   15,000,000.00               -15,000,000.00

So we have (for Model B-Model A) $$ (6,000,000 - 400,000) - 15,000,000(P/F, i^*,15) - 400,000(P/A,i^*,14) = 0 $$ or (for Model A-Model B) $$ -(6,000,000 - 400,000) + 15,000,000(P/F, i^*,15) + 400,000(P/A,i^*,14) = 0 $$ So at any rate we have to solve $$ 4(P/A,i^*,14) + 150(P/F, i^*,15) = 56 $$ and the IRR is $i^* ≈ 11.6\%$.

alexjo
  • 14,976