Question

1. A weekly magazine offers a 1-year subscription for $45 and a 3-year subscription for $118. If you read the magazine for at least the next 6 years, which type of subscription would you prefer if the interest rate is 10% over the next 6 years? Assume the subscription rate remains the same over the next 6 years. 2. The annual heat loss from the roof of a house is $520. You want to add some insulation on the roof to reduce your heating bill. Insulation A will cost $300 to install and is estimated to save 60% of the heat loss through the roof. Insulation B will cost $250 to install and is estimated to save 55% of the heat loss through the roof. Determine which insulation you will choose if you plan to live in the house for 10 years. Use an interest rate of 8%. 3. Using incremental benefit-cost ratio analysis, determine which one of the four mutually exclusive alternatives should be selected. Alt. A Alt. B Alt. C PWC PWB 100 124 400 422 200 231

Answer 1

1)

Let us assume that payments are made in the beginning of period

Present worth of 1 year subscription option=45*(P/A,0.10,6)*(1+0.10)

Let us calculate the interest factor

(1+i)" (P/A, i,n)=-

1- (1+0. 10) (Ρ/Α, 0.10, 6) = 4.3553 0.10

Present worth of 1 year subscription option=45*4.3553*1.10=$215.59

Present worth of 3 year subscription option=118+118*(P/F,0.10,3)

Let us calculate the interest factor

(P/F,0.10,3)=1/(1+0.10)^3=0.7513

Present worth of 3 year subscription option=118*+118*0.7513=$206.65

We can observe that 3-year option is cheaper. I shall prefer it.

2)

Annual savings of option A=520*60%=$312

NPW of option A=-300+312*(P/A,0.08,10)

1- (P/A, 0.08, 10) = - (1+0.10) = 6.7101 0.10

NPW of option A=-300+312*6.7101=$1793.55

Annual savings of option B=520*55%=$286

NPW of option A=-250+286*(P/A,0.08,10)

1- (P/A, 0.08, 10) = - (1+0.10) = 6.7101 0.10

NPW of option A=-250+286*6.7101=$1669.09

NPW of option A is higher. I shall prefer it.

3)

First we estimate incremental B-C ratio for each project by comparing with "Do nothing option, Ao"

Incremental B-C for A-Ao=(124-0)/(100-0)=1.24

Incremental B-C for B-Ao=(422-0)/(400-0)=1.055

Incremental B-C for C-Ao=(231-0)/(200-0)=1.155

We can observe that incremental B-C Ratio is higher than 1 in each case. So, all alternatives are better than "Doing nothing"

Now we calculate incremental B-C ratio for 2 alternatives with lowest costs

Incremental B-C for C-A=(231-124)/(200-100)=1.07

Incremetal B-C Ratio is higher than 1, we can go for alternative C

Now we calculate incremental B-C ratio for B-C

Incremental B-C for B-C=(422-231)/(400-200)=0.955

Incremetal B-C Ratio is less than 1, it is not worth to invest extra amount in alternative B.

We should select alternative C