Question

Questions 20-21 are based on the following information

Suppose that there is no origination cost. Given the following information,

        

            Option A:

                        Term: 30 years; Interest Rate: 5%; Discount Points: 0:

                        Homeowner will move in 2 years

     

            Option B:

                        Term: 30 years; Interest Rate: 5%; Discount Points: 1;

                        Homeowner will stay in the house for over 30 years

            Option C:

                        Term: 30 years; Interest Rate: 5.05%

                        Discount Points: 0; Homeowner will stay in the house for over 30 years

Which scenario has the lowest effective borrowing cost?

Option A

Option B

Option C

Not enough information

Which scenario has the highest effective borrowing cost?

Option A

Option B

Option C

Not enough information

Answer 1

Effective borrowing cost can be calculated from cash flows

Effective borrowing cost =Internal Rate of Return (IRR)of the cash flows

OPTION A

Nper

Term   in years

30

Rate

Interest Rate

5%

Pv

Amount of Loan ,assumed

$100,000

PMT

Annual payment

$6,505.14

(using PMT function of excel with Rate=5%, Nper=30, Pv=-100000)

Excel Command: PMT(5%,30,-100000)

FV1

Future value of Payments after 2 years

$13,335.54

(using FV function of excel with Rate=5%, Nper=2, Pmt=-6505.14)

Excel command: FV(5%,2,-6505.14)

FV2

Future value of Loan after 2 years

$110,250.00

(using FV function of excel with Rate=5%, Nper=2, Pv=-100000)

Excel command:FV(5%,2,,-100000)

FV2-FV1

Loan Balance at end of Year 2

$96,914.46

CASH FLOWS

Year

Cash Flow

0

($100,000)

1

$6,505.14

2

$103,419.60

(6505.14+96914.46)

Effective Borrowing Cost

5.00%

(Using IRR function of excel over the cash flow)

OPTION B

Nper

Term   in years

30

Rate

Interest Rate

5%

Amount of Loan ,assumed

$100,000

Payment for discount point

$1,000

(1%*100000)

PV

Net Cash Flow at year 0

$99,000

PMT

Annual payment for 30 years

$6,505.14

(using PMT function of excel with Rate=5%, Nper=30, Pv=-100000)

ExcelCommand:PMT(5%,30,-100000)

Terminal Payment at end of year 30

$0

RATE

Effective borrowing cost

5.0884%

(using RATE function of excel with Nper=30, Pmt=6505.14, Pv=-99000)

Excel Command : RATE(30,6505.14,-99000)

OPTION C

Nper

Term   in years

30

Rate

Interest Rate

5.05%

Amount of Loan ,assumed

$100,000

Payment for discount point

$0

(1%*100000)

PV

Net Cash Flow at year 0

$100,000

PMT

Annual payment for 30 years

$6,542.27

(using PMT function of excel with Rate=5.05%, Nper=30, Pv=-100000)

Excel Command: PMT(5.05%,30,-100000)

Terminal Payment at end of year 30

$0

RATE

Effective borrowing cost

5.05%

(using RATE function of excel with Nper=30, Pmt=6542.27.14, Pv=-100000)

Excel Command : RATE(30,6542.27,-100000)

Scenario with the lowest effective borrowing cost

OPTION: A

Scenario with the highest effective borrowing cost

OPTION: B