Chapter 22, Problem 12PS

a.

Summary Introduction

To determine: The present value of payoffs.

Answer to Problem 12PS

The present value of payoffs is $16,875,000.

Explanation of Solution

Determine the present value of payoffs

Excel Spreadsheet:

$\begin{array}{c}\mathrm{Pr}esentValueofPayoffs=\left[Payoff{s}_{Year0}\times Ratio\right]\\ =\left[\$18,000,000\times 93.75\%\right]\\ =\$16,875,000\end{array}$

Therefore the present value of payoffs is $16,875,000.

b.

Summary Introduction

To determine: The abandonment value.

Answer to Problem 12PS

The abandonment value is $1,936,448.60.

Explanation of Solution

Determine the gain value

The gain value is calculated if the demand is buoyant.

$\begin{array}{c}GainValue=\left[\left(\frac{Payoff{s}_{Year1}}{PVofPayoffs}\right)-1\right]\\ =\left[\left(\frac{\$22,500,000}{\$16,875,000}\right)-1\right]\\ =0.333333or33.33\%\end{array}$

Therefore the gain value is 33.33%.

Determine the loss value

The loss value is calculated if the demand is sluggish.

$\begin{array}{c}LossValue=\left[\left(\frac{Payoff{s}_{Year1}}{PVofPayoffs}\right)-1\right]\\ =\left[\left(\frac{\$15,000,000}{\$16,875,000}\right)-1\right]\\ =-0.11111or-11.11\%\end{array}$

Therefore the loss value is -11.11%.

Determine p

The value of put can be calculate using the risk neutral method, were p is identical to the probability of increase in the asset value.

$\begin{array}{c}rf=\left[\left(p\times GainValue\right)+\left(1-p\right)\times LossValue\right]\\ 7\%=\left[\left(p\times 33.33\%\right)+\left(\left(1-p\right)\times \left(-11.11\%\right)\right)\right]\\ p=0.408\end{array}$

Therefore p is 0.408.

Determine the abandonment value

If the demand is sluggish the payoffs will be $0 and if the demand is buoyant the payoffs is $3,500,000.

$\begin{array}{c}AbandonmentValue=\left[\frac{\left(p\times Payoff{s}_{Sluggish}\right)+\left(\left(1-p\right)\times Payoff{s}_{Buoyant}\right)}{\left(1+InterestRate\right)}\right]\\ =\left[\frac{\left(0.408\times \$0\right)+\left(\left(1-0.408\right)\times \left(\$18,500,000-\$15,000,000\right)\right)}{\left(1+7\%\right)}\right]\\ =\left[\frac{\$2,072,000}{1.07}\right]\\ =\$1,936,448.60\end{array}$

Therefore the abandonment value is $1,936,448.60.