Ann got a 30 year Fully Amortizing FRM for $600,000 at an annual interest rate o

Question

Ann got a 30 year Fully Amortizing FRM for $600,000 at an annual interest rate of 5% compounded annually with annual payments. After 2 years of payments, Ann will refinance the balance into a 28 year Fully Amortizing FRM at an annual interest rate of 3.5% compounded annually with annual payments. Refinancing will cost Ann 1.25 points plus $1250 in closing costs. Ann will prepay the new loan 3 years after refinancing.

The Annual payment before refinancing = 3903.09

The loan balance after 2 years = 581486.73

Annual payment after refinancing = 32913.69

The balance saving of a lower new loan balance= 7631.37

The cost of refinance= 8518.58

A. What's the final year total Cash Flow in the NPV formula for Ann’s refinancing decision (positive number)??

Needs to be correct by the cent!

Explanation / Answer

Lets calculate the annula payment for $600,000 for 30 years @5%. Enter the following int he financial calculator

PV = 600000; n=30; 1/y = 5%; FV = 0; calculate PMT = $39,030.86

Now out of this, first year interest is 5%*600000 = $30,000 and thus remaining $9,030.86 is the principle payment.

End of year principle is 600000-9030.86 = $590,969.14

Now second year interest is 5%*590,969.14 = $29,548.46 and thus remining (39030.86-29548.46) $9,482.4 will be the principle component paid and thus Principle outstanding after 2 years will be $590,969.14 - $9,482.4 = $581,486.74

Now again to caluclate the annual repayment input the following int he financial calculator

PV = 581,486.74; FV = 0; 1/y = 3.5%; n = 28; calculate PMT = $32,913.69

Cost of refinancing is 1.25%*581486.74 + 1250 = $8518.58

Savings is $39,030.86 - $32,913.69 = $6,117.17

Now this loan is to be paid 3 years after refinancing.

Using PPMT function in excel, lets calculate the principle payment in year 1 , 2, and 3

PPMT(3.5%,1,28,581486.73) = 12,561.65

PPMT(3.5%,2,28,581486.73) = 13,001.31

PPMT(3.5%,3,28,581486.73) = 13,456.36

Total principle paid is $39,019.32

Now final year total cash flow is 581486.74 - 39019.32 = $542,467.42

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