Question

The NPVs of project proposals A and B are: \[ NPV_A = -0.01i^2 - 0.02i + 4.44, \qquad NPV_B = -0.03i^2 - 0.01i + 6.55, \] where $i$ is the discount rate. The discount rate for which both proposals have equal possibility of acceptance or rejection (rounded off to two decimals) is __________.

Hint:

The point of equal NPV indicates equal likelihood of choosing either project.

Answer 1

Correct Answer: 10

Set the two NPVs equal:
\[ -0.01i^2 - 0.02i + 4.44 = -0.03i^2 - 0.01i + 6.55. \]
Bring all terms to one side:
\[ 0.02i^2 - 0.01i - 2.11 = 0. \]
Divide by 0.02:
\[ i^2 - 0.5i - 105.5 = 0. \]
Solve quadratic:
\[ i = \frac{0.5 \pm \sqrt{0.25 + 422}}{2}. \]
\[ i = \frac{0.5 \pm \sqrt{422.25}}{2} = \frac{0.5 \pm 20.556}{2}. \]
Positive root (only meaningful):
\[ i = \frac{0.5 + 20.556}{2} = 10.528. \]
Rounded:
\[ \boxed{10.53} \quad (\text{acceptable range: } 10.00\text{–}11.00) \]