In: Finance

# You are considering investment in one of the following two options. Assume an interest rate of...

You are considering investment in one of the following two options. Assume an interest rate of 12% per year, compounded monthly. Option A & Option B

Initial Cost, respectively
-$100,000 -$800,000
Quarterly Maintenance Cost, respectively
-$26,000 -$15,000
Salvage Value, respectively
$16,000$200,000
Lifespan (years) 2 & 4, respectively

a. What is the effective monthly interest rate?

b. What is the effective quarterly interest rate (to 2 decimal places)?

c. Draw cash flow diagrams for the two projects.

d. Calculate the PW of the 2 options, assuming repeatability. Which option would you choose?

e. Calculate the quarterly worth of the 2 options (AW). Which option would you choose?

## Solutions

##### Expert Solution

a. Formula for Effective Annual Interest Rate = ((1+i/n)^n)−1

Here i=Nominal interest rate

n=Number of periods​ of compounding

So putting the given figure here, we get = ((1+ 12%/12)^12)-1

Solving above we get = 12.68%

So effective monthly Interest will be = 12.68%/12 = 1.06%

b.

Effective Quarterly Interest Rate(Based on monthly compounding) = 12.68%/4 = 3.17%

c. Below are the cash flow of the project assming no repeatablity.

 Option A Option B Initial cost -100000 -800000 Y1Q1 -26000 -15000 Y1Q2 -26000 -15000 Y1Q3 -26000 -15000 Y1Q4 -26000 -15000 Y2Q1 -26000 -15000 Y2Q2 -26000 -15000 Y2Q3 -26000 -15000 Y2Q4 -10000 -15000 Y3Q1 0 -15000 Y3Q2 0 -15000 Y3Q3 0 -15000 Y3Q4 0 -15000 Y4Q1 0 -15000 Y4Q2 0 -15000 Y4Q3 0 -15000 Y4Q4 0 185000

d. Below is the calculation of Present worth of Option A and Option. We will choose option A, as this option will incurred the less cost.

Formual for Present value = 1/(1+r)^n. Here r = Rate per period (i.e. quarter) which is  3.17%

n= 1,2,3.....

 Option A Present Value Option B Present Value Initial Value -100000 -100000 -800000 -800000 Y1Q1 -26000 -25201 -15000 -14539 Y1Q2 -26000 -24427 -15000 -14092 Y1Q3 -26000 -23676 -15000 -13659 Y1Q4 -26000 -22949 -15000 -13240 Y2Q1 -26000 -22244 -15000 -12833 Y2Q2 -26000 -21560 -15000 -12439 Y2Q3 -26000 -20898 -15000 -12056 Y2Q4 -110000 -85697 -15000 -11686 Y3Q1 -26000 -19633 -15000 -11327 Y3Q2 -26000 -19030 -15000 -10979 Y3Q3 -26000 -18445 -15000 -10642 Y3Q4 -26000 -17879 -15000 -10315 Y4Q1 -26000 -17329 -15000 -9998 Y4Q2 -26000 -16797 -15000 -9690 Y4Q3 -26000 -16281 -15000 -9393 Y4Q4 -10000 -6069 185000 112284 -478115 -864603

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