Question

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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