Chapter 2, Problem 28PS

a.

Summary Introduction

To determine: The present value at the end of each year.

Answer to Problem 28PS

The present value at the end of each year is $12.50 billion.

Explanation of Solution

Determine the present value at the end of each year

$\begin{array}{c}\mathrm{Pr}esentValue=\left[\frac{AmountofInvestment}{InterestRate}\right]\\ =\left[\frac{\$1billion}{8\%}\right]\\ =\$12.50billion\end{array}$

Therefore the present value at the end of each year is $12.50 billion.

b.

Summary Introduction

To determine: The present value at the end of first year if the growth rate is 4%.

Answer to Problem 28PS

The present value at the end of first year if the growth rate is 4% is $25 billion.

Explanation of Solution

Determine the present value at the end of first year if the growth rate is 4%

$\begin{array}{c}\mathrm{Pr}esentValue=\left[\frac{AmountofInvestment}{\left(InterestRate-GrowthRate\right)}\right]\\ =\left[\frac{\$1billion}{\left(8\%-4\%\right)}\right]\\ =\$25billion\end{array}$

Therefore the present value at the end of first year if the growth rate is 4% is $25 billion.

c.

Summary Introduction

To determine: The present value at the end of 20 years.

Answer to Problem 28PS

The present value at the end of 20 years is $9.82 billion.

Explanation of Solution

Determine the present value at the end of 20 years

Excel Spreadsheet:

Therefore the present value at the end of 20 years is $9.82 billion.

d.

Summary Introduction

To determine: The present value if spread evenly for 20 years.

Answer to Problem 28PS

The present value if spread evenly for 20 years is $10.20 billion.

Explanation of Solution

Determine the continuous compounded rate

$\begin{array}{c}ContinuousRate=\left[LN\left(1+Rate\right)\right]\\ =\left[LN\left(1+8\%\right)\right]\\ =7.70\%\end{array}$

Therefore the continuous compounded rate is 7.70%.

Determine the present value if spread evenly for 20 years

$\begin{array}{c}\mathrm{Pr}esentValue=\left[AmountInvested\times \left(\frac{1}{Rate}\right)-\left(\frac{1}{\left(Rate\times e^{rt}\right)}\right)\right]\\ =\left[\$1billion\times \left(\frac{1}{7.70\%}\right)-\left(\frac{1}{\left(7.70\%\times {2.71828}^{\left(7.70\%\times 20\right)}\right)}\right)\right]\\ =\left[\$1billion\times 12.98701-2.784173\right]\\ =\$10.20284billionor\$10.20billion\end{array}$

Therefore the present value if spread evenly for 20 years is $10.20 billion.