Question

Derek and Meagan Jacoby recently graduated from State University and Derek accepted a job in business consulting while Meagan accepted a job in computer programming. Meagan inherited $32,000 from her grandfather who recently passed away. The couple is debating whether they should buy or rent a home. They located a rental home that meets their needs. The monthly rent is $2,350. They also found a three-bedroom home that would cost $112,000 to purchase. The Jacobys could use Meagan’s inheritance for a down payment on the home. Thus, they would need to borrow $80,000 to acquire the home. They have the option of paying two discount points to receive a fixed interest rate of 4.50 percent on the loan or paying no points and receiving a fixed interest rate of 5.75 percent for a 30-year fixed loan. Though anything could happen, the couple expects to live in the home for no more than five years before relocating to a different region of the country. Derek and Meagan don’t have any school-related debt, so they will save the $32,000 if they don’t purchase a home. Also, consider the following information: The couple’s marginal tax rate is 24 percent. Regardless of whether they buy or rent, the couple will itemize their deductions. If they buy, the Jacobys would purchase and move into the home on January 1, 2018. If they buy the home, the property taxes for the year are $3,700. Disregard loan-related fees not mentioned above. If the couple does not buy a home, they will put their money into their savings account where they earn 5 percent annual interest. Assume that all unstated costs are equal between the buy and rent option. Required: Help the Jacobys with their decisions by answering the following questions: (Leave no answer blank. Enter zero if applicable.)

1. What is the approximate break-even point in years for paying the points to receive a reduced interest rate? (To simplify this computation, assume the Jacobys will make interest-only payments, and ignore the time value of money.) (Do not round intermediate calculations. Round your final answer to 1 decimal place.)

2. What is the after-tax cost (in interest and property taxes) of living in the home for 2018? Assume that the Jacobys' interest rate is 5.75 percent, they do not pay discount points, they make interest-only payments for the first year, and the value of the home does not change during the year. (Round your intermediate calculations to the nearest whole dollar amount.)

3. Assume that on March 1, 2018, the Jacobys sold their home for $133,000, so that Derek and Meagan could accept job opportunities in a different state. The Jacobys used the sale proceeds to (1) pay off the $80,000 principal of the mortgage, (2) pay a $10,000 commission to their real estate broker, and (3) make a down payment on a new home in the different state. However, the new home cost only $60,000. Assume they make interest-only payments on the loan.

Required:

3(1). What gain or loss do the Jacobys realize and recognize on the sale of their home?

3(2). What amount of taxes must they pay on the gain, if any?

Answer 1

1. The question says ignore time value of money and assume interest only payments.

So Yearly payment at 5.75% interest rate = $80000*0.0575 = $4600

Yearly payment at 4.5% interest rate = $80000*0.045/12 = $3600

Hence, Yearly saving due to the reduced interest rate = $4600-$3600 = $1000

Cost of 2 points = 2%*$80000 = $1600 (1 point = 1% of the loan amount)

So break-even (in years) = $1600/$1000 = 1.6 years

2.

Loan amount = $80000

Marginal Tax rate = 24%

Interest Rate (without points) = 5.75%

So Yearly payment at 5.75% interest rate = $80000*0.0575 = $4600

Tax savings from interest payments = 24%*4600 = $1104

Property Tax = $3700

Tax Savings from property taxes = 24%*3700 = $888

So After Tax cost for 1st year = $4600-$1104+$3700-$888 =$6308

3.

Sale Price = $133,000

Agent Commission = $10000

Net Sale Price = $133000-$10000 = $123000

Mortgage Amount = $80000

Recognized Gain = $123000-$80000-$32000 = $11000

Tax = 24%*11000 = $2640

Realised Gain = $11000-2460 = $8360