Chapter 8, Problem 24P

To determine

i.

Interest Rates preferred for each payment plan.

Answer to Problem 24P

Interest rate	Best Choice
0%	Alternative D
17.84%	Alternative A

Explanation of Solution

Given:

Availability of Magazine for $58 for 1 year

Availability of Magazine for $108 for 2 year

Availability of Magazine for $153 for 3 year

Availability of Magazine for $230 for 5 year.

Calculation:

There are four alternatives available for payment.

Year	A	B	C	D	D-A
1	-58	-108	-153	0	58
2	-58	0	0	0	58
3	-58	-108	0	-230	-172
4	-58	0	-153	0	58
5	-58	-108	0	0	58
6	-58	0	0	-230	-172
7	-58	-108	-153	0	58
8	-58	0	0	0	58
9	-58	-108	0	-230	-172
10	-58	0	-153	0	58
11	-58	-108	0	0	58
12	-58	0	0	-230	-172
13	-58	-108	-153	0	58
14	-58	0	0	0	58
15	-58	-108	0	-230	-172
16	-58	0	-153	0	58
17	-58	-108	0	0	58
18	-58	0	0	-230	-172
19	-58	-108	-153	0	58
20	-58	0	0	0	58
21	-58	-108	0	-230	-172
22	-58	0	-153	0	58
23	-58	-108	0	0	58
24	-58	0	0	-230	-172
25	-58	-108	-153	0	58
26	-58	0	0	0	58
27	-58	-108	0	-230	-172
28	-58	0	-153	0	58
29	-58	-108	0	0	58
30	-58	0	0	-230	-172

The number of periods extended to 30 years because of different useful life. One alternative is available for 5 years and other is for 3 years and another one is available for 2 years. So, the least common factor is 1,2,3 and 5 is 30. This table represents the cash flow of all the four alternatives. Negative value means cash outflow and zero value means neither cash inflow nor cash outflow.

Graph of net present worth of all four alternatives versus interest rate.

Graph:

The graph clears the picture and explains that the alternative C and D are not part of the answer. Only alternative A and D is important.

Net Present worth of (Alternative B)-(Alternative A):

$\begin{array}{l}NPW=-P+A(P/A,i,n)-F_1(P/F_1,i,n)-F_2(P/F_2,i,n)-F_3(P/F_3,i,n)\\ -F_4(P/F_4,i,n)\end{array}$

P = initial Cost

A = annual payment that is uniform all the period

F₁ = Future value in 6^th year

F₂ = future Value in 11^th year

F₃ = Future Value in 16^th year

F₄ = future value in 21^st year

F₅ = Future Value in 26^th year

I = rate of return

N = time period

P	A	F1	F2	F3	F4	F5	i	n
$172	$58	$230	$230	$230	$230	$230	?	$30

Time period

6 for F₁

11 for F₂

16 for F₃

21 for F₄

26 for F₅

$\begin{array}{l}0=-\$172+\$58(P/A,i,30)-\$230(P/F_1,i,6)-\$230(P/F_2,i,11)\\ -\$230(P/F_3,i,6)-\$230(P/F_4,i,6)-\$230(P/F_5,i,6)\end{array}$

Interest rate	(P/A,i,30)	(P/ F1,i,6)	(P/ F2,i,11)	(P/ F3,i,16)	(P/ F4,i,21)	(P/ F5,i,26)
15.00%	6.566	0.4343	0.2149	0.1069	0.0531	0.0264
18.00%	5.571	0.3704	0.1619	0.0708	0.0309	0.0135

The rate of return, which is between 15% and 18% is computed by linear interpolation:

$IRR=i{\%}_{low}+(i{\%}_{high}-i{\%}_{low})\left[\frac{F_{low}-P}{F_{low}-F_{high}}\right]$

$i{\%}_{low}$ = Lower interest rate

$i{\%}_{high}$ = Higher interest rate

$F_{low}$ = factor of lower interest rate

$F_{high}$ = factor of higher interest rate

$IRR=15\%+(18\%-15\%)\left[\frac{\$189.1-\$172}{\$189.1-\$172-(\$171.06-\$172)}\right]$

$IRR=15\%+3\%\left[\frac{\$17.1}{\$18.039}\right]$

$IRR=15\%+3\%\times 0.9479$

$IRR=15\%+0.02843$

$IRR=0.17843$

Therefore, the incremental rate of return is 17.84%.

Conclusion:

Choice Table:

Interest rate	Best Choice
0%	Alternative D
17.84%	Alternative A

To determine

ii.

Impact on environment due to glossy paper of magazine.

Answer to Problem 24P

1. Lead to highest destruction of forest which had been sustainably managed. As magazine requires higher-grade paper.
2. Glossy paper of magazine results in contamination of recycling process of paper.
3. Ultraviolet sealing coating on glossy paper complicated recycling of paper.
4. Glossy papers are made with toxic chlorine, which leads to soil pollution.

Explanation of Solution

Given:

Subscription of Magazine with different plans.

Concept used:

Lead to highest destruction of forest which had been sustainably managed. As magazine requires higher-grade paper.

Glossy paper of magazine results in contamination of recycling process of paper.

Ultraviolet sealing coating on glossy paper complicated recycling of paper.

Glossy papers are made with toxic chlorine, which leads to soil pollution.

Conclusion:

Lead to highest destruction of forest which had been sustainably managed. As magazine requires higher-grade paper.

Glossy paper of magazine results in contamination of recycling process of paper.

Ultraviolet sealing coating on glossy paper complicated recycling of paper.

Glossy papers are made with toxic chlorine, which leads to soil pollution.