So here are some problems I\'m having issues with. If you can help it would be a

Question

So here are some problems I'm having issues with. If you can help it would be appreciated.

An engineer wishes to buy a house but can only afford monthly payments of $1500. 30-year loans are available at 5.75% yearly interest compounded monthly. If the engineer can make a $20,000 down payment, what is the price of the most expensive house that the engineer can afford to purchase? Calculate the net present value (NPV) and annual equivalent value (AE) of the following cash flow diagram. The Minimum Acceptable Rate of Return (MARR) is 15%. Calculate the IRR for the cash flow diagram. Calculate the ERR for the cash flow diagram. Determine whether an investment made according to this cash flow is more profitable than "doing nothing" and just collecting the MARR. Explain your answer.

Explanation / Answer

SOLUTION :

3..PV = PMT x [(1 – (1+r) -N )) / r]

PMT=MONTHLY PAYMENT=1500, PV = PRESENT VALUE, r = interest rate=.0.0575/12, n=number of payment =30x12=360

PV =1500 x (1 – (1+.0575/12) -360 )) /(.0575/12)

=257037.31

Most expesive house that can afford = PV + downpayment

=257037.31 + 20000

=277037.31

4..

a

NPV

year

cash flow

DF @15%

PV

0

-2500

1

- 2,500.00

1

500

0.86956522

      434.78

2

650

0.75614367

      491.49

3

800

0.65751623

      526.01

4

800

0.57175325

      457.40

5

800

0.49717674

      397.74

6

800

0.4323276

      345.86

7

800

0.37593704

      300.75

NPV

      454.04

equivalent annual cash flow = NPVxr /(1-(1+r)^-7

454.04x.15/(1-(1.15^-7)

109.13

b.

IRR

20.40%

year

cash flow

DF @20.40%

PV

0

-2500

1

- 2,500.00

1

500

0.83059416

      415.30

2

650

0.68988666

      448.43

3

800

0.57301583

      458.41

4

800

0.4759436

      380.75

5

800

0.39531597

      316.25

6

800

0.32834714

      262.68

7

800

0.27272321

      218.18

NPV

           0.00

C

ERR = 15%

d

Yes the investment made is more profitable than collecting MARR as it has Positive NPV

a

NPV

year

cash flow

DF @15%

PV

0

-2500

1

- 2,500.00

1

500

0.86956522

      434.78

2

650

0.75614367

      491.49

3

800

0.65751623

      526.01

4

800

0.57175325

      457.40

5

800

0.49717674

      397.74

6

800

0.4323276

      345.86

7

800

0.37593704

      300.75

NPV

      454.04

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