Case Summary Studebaker had spared a considerable amount of money in excess of $30,000 that was in mutual funds. His mortgage balance was $45,000 with an annual rate of 7% and a yearly payment of 4,248 with 20 years remaining. Morton advised Studebaker to get a new mortgage so that he could unlock $25,000 of equity. This, he explained, would accumulate $176,392 in twenty years, factoring in the $30,000 that he would have to invest in a single-premium insurance policy. He was assured of getting a yearly 6% return as opposed to the 5% that he was getting at that time. However, the new investment strategy would have a downside, as mortgage payments would increase by $3,052, from $4,248 to $7,300. However, the yearly earnings from the life insurance policy would surpass the increase in cost, as the first year was estimated to increase by $3,300, from $55,500 to $58,800. Over the 20-year period, the earnings were expected to increase by $9,984.Studebaker decided to seek a second opinion, and he contacted Phyllis Corner, who worked in the economics department. Corner identified errors in Morton’s assumptions such as the omission of taxes, $5,000 fees involved in moving Studebaker’s equity into equity into insurance policy, increase in mortgage from 7% to 9%, and the problem of getting an unnecessary life policy as other long-term investments would also give out similar returns. She advised that the $30,00 and the $3,052 increase in annual mortgage could be invested in other investments that would earn higher returns. She stressed upon the importance of considering lost opportunities for accruing interest on the $30,000, and for the additional mortgage payments amounting to $3,052 that would have been invested elsewhere, therefore earning interest.
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Questions Answer 1. Morton notes that the $55,000 invested in the single-premium life insurance policy would grow to $176,392 in 20 years for a return of 6% per year. Explain how this return was calculated. Answer:
FV N= PV(1 + I) N =55,000(1+6%)20 =$176,392 The $55,000 was derived from the $30,000 that Baker had invested in a money market mutual fund and the $25,000 that he would likely save by getting a new mortgage. The yearly earnings from the life insurance policy amounted to 6%. As such, the policy accrues accumulation value each year for 20 years. The first year accrues $3,300, an amount that is added to the initial policy payment of $55,000 to make up $58,300. The policy value increases each year to reach $176,392 in the 20th year. The rate is calculated in a compounding basis so as to determine the future value of a cash flow.
2. In order to re-position the equity in his home, Studebaker would have to take out a 30year, $75,000 mortgage at 9 percent. Explain how the yearly mortgage payments on this loan were obtained. Answer: PV= FV N /(1 + I) N
=$75,000/(1+9%)30 =$5,651.7 The 9% was arrived at after calculating the present value of a cashflow with regards to the present purchasing power. The process is known as discounting as it shows the value of the cash flows after factoring in today’s purchasing power.
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3. For the 9% mortgage in Exhibit 4, find the loan balance at the end of years 19 and 20.
Loan Amortization Schedule, 9% Interest rate. Year
Beginning Amount(1)
Payment(2)
Interest(3)
19 20
24500.88 22325.76
4380.12 4380.12
2205 2009.32
Payment of Remaining Principle(2)Balance(1)(3)=(4) (4) 2175.12 22325.76 2370.80 19954.96
Given, PV= $45000 n= 30 i=9% (Compounded Yearly) Here, PMT=PV/(PVIFA, i, n) =$45,000/10.2737 =$4,380.12 4. Exhibit 3 indicates that $176,392 will be accumulated after 20 years in the life insurance policy. Is this really true? (Hint: If Studebaker were to make this investment, how would his debt position look like in 20 years?)
Answer: Yes, it would be true when payment rate would be 6%. If we calculate the payment policy in annuity basis policy payment would be $55,000. 5.(a) If the excess $30,000 were invested in a long-term asset yielding 8 percent a year, how much would be accumulated after 20 years?
Given, PV= $30,000 i=8% n=20 Now, FV20= PV (1+0.08)20 3
=$30000*4.66 = $139,828.71 So after 20 years $139828.71 is accumulated. 5. (b) Suppose Studebaker placed $3,052 a year into long-term investment paying 8% a year. How much would be accumulated after 20 years (amounts invested at the end of each year)?
Here, FV20=$3052(1+0.08)20 =$14225.24 So, at the end of 20 years the amount will be $14225.24 6. Repeat problem 5 but assume a 7% return can be earned. (a)
Given, PV= $30,000 i=7% n=20 Now, FV20= PV (1+0.07)20 =$30,000*3.8697 =$116,090.53 So, after 20 years the accumulated balance is $116,090.53 (b)
Here, FV20=$3,052(1+0.07)20 =$11,810.28 So, at the end of 20 years the amount will be $11,810.28 4
7. Comer’s criticism implied that the single life-insurance policy is unattractive investment for Studebaker. What do your previous answers suggest?
Single life insurance policy is unattractive because of the following reasoni) The insurance costs too much: When a whole life insurance policy is sold (and they’re always sold, never bought), the buyer and seller generally focus on the investment portion of the policy, not the insurance policy. The silly buyer just naturally assumes he’s getting the insurance portion at the going rate (such as what he would pay for term insurance.) Fool. Like any business, they charge what they can get away with. If you’re not paying attention, you’d better believe the price gets jacked up. A bigger problem is that young people can’t afford enough whole life insurance to cover their actual need for insurance, so they end up buying a separate term policy anyway, or worse, they don’t and walk around under -insured. ii) The fees are too high: We don’t pay the fees directly, but we do pay them with lower returns. For example, the commission on a whole life insurance policy is generally 100% of the first year’s premiums then 6% of premiums every year after that. That’s money that doesn’t get invested on your behalf. By comparison, the commission on a term policy is about 50% of the first year’s premiums, then 4% of premiums after that. It’s pretty easy to see what the financial incentive is. Sell whole life instead of term, and upgrade the policy at every opportunity. 100% of a new policy is far better than 6% of an old one. “But you don’t pay the commissions, the company does” argues the salesman. Where do you suppose the company gets the money from? iii) Complexity favors the issuer: After a while, people figured out that whole life insurance was a rip-off. So to disguise that fact, the companies just made the products so complex that only their actuaries could figure them out. Even those who have spent a great deal of time trying to figure these policies out don’t understand them. Even the guys selling them don’t completely understand them, but you better believe they understand the commission structure. Suffice to say, the more complex it gets, the worse a deal it is for you. 8.(a) Suppose Studebaker’s goal is to accumulate $400,000 in 20 years. Assumed $30,000 invested at 8% interest. How much will he have to save in equal amount at the end of each year of the next 20 years if he can earn 8% of any investment?
Here Given, FVA=$400,000 n=20 We know, FVA=C*{(1+i)n-1/i} So, C= FVA/{(1+i)n-1/i} =$400,000/45.76 =$8740.88
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So, he need to save overall $8740.88 per year if he wants to accumulate the balance is $400,000. Now, $30,000 at 8% interest Per year interest= $30000*8% =$2400 So, Studebaker needs to save at the end of each year = ($8740.88-$2400) =$6340.88 8.(b) Repeat part (a) but assume he will not be able to save any money in years 13 to 20, this is he will save an equal amount at the end of years 1 to 12 and nothing thereafter.
Based on previous the total save amount= $8,740.88*20 =$174,817.6 So, Studebaker needs to save per year= $174,817.6/12 =$14,568.13 He gets per year interest = $2400 So, Studebaker needs to save at the end of each year= ($14,568.13-$2400) =$12,168.13 9. The yearly payment on the new 30-year, $75,000 mortgage is $7,300. This assumes one payment is made at the end of each of the next 30-years. Suppose that payments must be made at the end of each month. Would 12 of these monthly payments be equal to one of the yearly payments? Explain.
No, there is difference between monthly payment and yearly payment. Monthly payment is higher than the yearly payment. Suppose, Mr. X invest $1000 and it gives 10% interest yearly. So, FV=$1000(1+.1)1 =$1100 6
If the same amount invest on monthly interest basis then FV=$1000(1+.1/12)1*12 =$1104.71 Here, we clearly see that there is difference between yearly payment & monthly payment. 10. Exhibit 3 suggests that the annual cost of the life insurance policy is $3, 052. With the adjustments mentioned in the case, Comer calculated the cost to be $5,152 in Year 1 and $18,632 by year 20 assuming a 7% annual return. Explain how these were determined. Answer: The annual cost of the insurance amounting to $3,052 was added to $2,100 of lost
interest to amount to $5,152. Comer assumed that the $30,000 that would be invested in the life insurance policy, therefore losing the interest that would have been earned on it. The cost could have inflated to $18,632 by year 20 due to compounding interest that would have been earned on $5,152.
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