In: Finance

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?

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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