Chapter 5, Problem 18P

a.

Summary Introduction

To calculate: Present value of cash flow stream at 5% discounting rate.

Present value of cash flow:

It is also called as discounted value. It defines that amount of money that invested at a given rate of interest will increases the amount of future cash flow at that particular time in future.

Explanation of Solution

Calculation of present value of cash flow stream at 5% discounting rate

Year	Discounting Rate	Cash Flows		Present value of cash flows
		Stream A	Stream B	Stream A (B×C)	Stream B (B×D)
A	B	C	D	E	F
0	1.000000	0	0	0	0
1	0.952381	150	250	142.8572	238.0953
2	0.907029	450	450	408.1631	408.1631
3	0.863838	450	450	388.7271	388.7271
4	0.822702	450	450	370.2159	370.2159
5	0.783526	250	150	195.8815	117.5289
		Present value for Stream A and Stream B		1505.845	1522.73

Table (1)

Working Note to calculate discounting rate

Formula to calculate discounting rate for year 1

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.05\right)}^1}\\ =0.952381\end{array}$

Formula to calculate discounting rate for year 2

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.05\right)}^2}\\ =0.907029\end{array}$

Formula to calculate discounting rate for year 3

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.05\right)}^3}\\ =0.863838\end{array}$

Formula to calculate discounting rate for year 4

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.05\right)}^4}\\ =0.822702\end{array}$

Formula to calculate discounting rate for year 5

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.08\right)}^5}\\ =0.783526\end{array}$

Conclusion

Present value for Stream A and Stream B is $1,505.84 and $1,522.73, respectively.

b.

Summary Introduction

To calculate: Present value of cash flow stream at 0% discounting rate.

Present value of cash flow:

It is also called as discounted value. It defines that amount of money that invested at a given rate of interest will increases the amount of future cash flow at that particular time in future.

Explanation of Solution

Calculation of present value of cash flow stream at 0% discounting rate

Year	Discounting Rate	Cash Flows		Present value of cash flows
		Stream A	Stream B	Stream A $\text{B}\times \text{C}$	Stream B $\text{B}\times \text{D}$
A	B	C	D	E	F
0	1.000000	0	0	0	0
1	1.000000	150	250	150	250
2	1.000000	450	450	450	450
3	1.000000	450	450	450	450
4	1.000000	450	450	450	450
5	1.000000	250	150	250	150
		Present value for Stream A and Stream B		1,750	1,750

Table (2)

Working Note to calculate discounting rate

Formula to calculate discounting rate for year 1

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.00\right)}^1}\\ =1.0000\end{array}$

Formula to calculate discounting rate for year 2

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.00\right)}^2}\\ =1.0000\end{array}$

Formula to calculate discounting rate for year 3

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.00\right)}^3}\\ =1.0000\end{array}$

Formula to calculate discounting rate for year 4

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.00\right)}^4}\\ =1.0000\end{array}$

Formula to calculate discounting rate for year 5

$\begin{array}{c}\text{Discount}\text{Rate}=\frac{1}{{\left(1+\text{Interest}\text{rate}\right)}^{\text{Number}\text{of}\text{years}}}\\ =\frac{1}{{\left(1+0.00\right)}^5}\\ =1.0000\end{array}$

Conclusion

Present value for Stream A and Stream B is $1,750 and $1,750 respectively.