a firm is considering a project that has an initial cost today of $14,000. the project has a life of two…

Explanation:

Step1: Calculate the future - cost of the project

The initial cost of the project today is $C_0 = 14000$. It will increase by 3% in two years. The future - cost formula is $C_2=C_0(1 + g)^n$, where $g = 0.03$ and $n = 2$. $C_2=14000\times(1 + 0.03)^2=14000\times1.03^2=14000\times1.0609 = 14852.6$

Step2: Calculate the present - value of the future cash inflows

The cash inflows are $A = 11000$ per year for 2 years starting 2 years from now. First, find the present - value of the annuity at the start of year 2. The formula for the present - value of an ordinary annuity is $PV_{A2}=A\times\frac{1-(1 + r)^{-n}}{r}$, where $A = 11000$, $r=0.12$, and $n = 2$. $PV_{A2}=11000\times\frac{1-(1 + 0.12)^{-2}}{0.12}=11000\times\frac{1 - 0.797194}{0.12}=11000\times\frac{0.202806}{0.12}=11000\times1.69005=18590.55$ Then, discount this value back to the present. The present - value of $PV_{A2}$ today is $PV_{A0}=PV_{A2}\times(1 + r)^{-2}=18590.55\times(1 + 0.12)^{-2}=18590.55\times0.797194\approx14815.46$

Step3: Calculate the value of the option to wait

The value of the option to wait is the present - value of the future cash inflows minus the present - value of the future cost. The present - value of the future cost is $PV_{C0}=C_2\times(1 + r)^{-2}=14852.6\times(1 + 0.12)^{-2}=14852.6\times0.797194\approx11839.92$ The value of the option to wait $V=PV_{A0}-PV_{C0}=14815.46 - 11839.92=1935.54$

Answer:

$1,935.54$