Question

Albert Einstein reportedly said, “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.” Regardless of whether Einstein uttered these exact words, the essence of his statement is still immensely powerful and cannot be disputed. For anyone who wants to build lasting wealth, understanding and harnessing the power of compound interest is essential. For the more visual of you, imagine, if you will, building the bottom part of a snowman. It starts with a snowball (or initial investment). You roll it around in the snow and it slowly gets bigger (interest on the investment). A slow and monotonous process until something wonderful becomes apparent – the snowball not only gets bigger and bigger, but at a faster and faster rate (interest on the interest).

Your friend, Mike Szyslak wants be a millionaire, and he found several ways applicable. But he is still hesitating among the various options and comes to you for financial advice. Complete each of the options, below, with your group.

• Option 1: He is considering to buy Mega Millions lottery. If the current tax rate on earnings of lottery is 40%, how much money will he have to win on a lottery to become a millionaire?
• Option 2: His uncle promised to invest his business $100,000 a year over the next 15 years, and the interest rates over next 15 years are expected be at 5% per annual. Can you help him to know whether the present value of such series of investments make him equivalent to be a millionaire today?
• Option 3: He considers to save money and become a millionaire. Starting at age 22, every night Mike takes $5 out of your pocket and put it in a manila envelope. At the end of the year, you place the money from the envelope in a stock fund with an average interest rate of 10%. Will the amount he has in the account ensure him a millionaire when you retire at age 65? What if he starts saving at age 40?
• Option 4: He sets aside $50,000 into a saving account now, and will deposit $50,000 into the account at the beginning of each year for next 10 years. If the market rate is 10%, Will he become a millionaire in 10 years?
• Option 5: Mike considers to buy 1,000 bonds. The bond is semi-annual coupon bond with 10-year maturity, $1,000 par value bond with a 10 percent annual coupon, and 10 percent annual required rate of return? How much does it cost now if he wants to receive all the coupon payments and par values during the 10-year period? What would be the value of the bond if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing Mike to require a 13 percent return? What would happen to the bonds' value if inflation fell, and required rate of return declined to 7 percent?

Which of the options would you recommend that Mike choose? Why?

You may use algebra, TVM tables, financial calculator, or Excel to solve these problems, and present a report to explain the concept of Time Value of Money.

Answer 1

Option 1)

He wants earnings on lottery after tax of $1,000,000.

Total lottery winnings = "x"; tax rate = 0.4

Total lottery winnings*(1-tax rate) = earnings on lottery after tax

x*(1-0.4) = 1,000,000

x*0.6 = 1,000,000

x = 1,000,000/0.6

x = 1,666,667

He has to win $1,666,667 on a lottery to become a millionaire.

Option 2) Yes, Present value of such series of investments make him equivalent to be a millionaire today.

Year	Investment	Present value factor @ 5%	Discounted cash flow
1	100,000	0.9524	95,238
2	100,000	0.9070	90,703
3	100,000	0.8638	86,384
4	100,000	0.8227	82,270
5	100,000	0.7835	78,353
6	100,000	0.7462	74,622
7	100,000	0.7107	71,068
8	100,000	0.6768	67,684
9	100,000	0.6446	64,461
10	100,000	0.6139	61,391
11	100,000	0.5847	58,468
12	100,000	0.5568	55,684
13	100,000	0.5303	53,032
14	100,000	0.5051	50,507
15	100,000	0.4810	48,102
PV of Investment	1,037,966

Option 3) Starting to invest at age 22 make him millionaire at age 65. While starting at age 40 doesn't.

Let assume total number of days in a year = 365days (ignore leap year)

Savings per year = $5*365 = $1,825

Option 4) No, he will not become millionaire. He earns only $876,558.35 at the end of year 10.

Option 5)

Since the bond coupon rate is equal to required rate of bond, value will be equal to par. So cost of the bond is $1,000 (equal to par value).

Price of the bond = 834.72 (when required rate of return = 13%) (Note: Since coupon is paid semi-annually, required raturn is converted into per 6-months i.e. 13%/2 = 6.5%)

Year	Type	Cashflow	Present value factor @ 6.5%	Discounted cash flow
0.5	Coupon	50	0.9390	46.95
1.0	Coupon	50	0.8817	44.08
1.5	Coupon	50	0.8278	41.39
2.0	Coupon	50	0.7773	38.87
2.5	Coupon	50	0.7299	36.49
3.0	Coupon	50	0.6853	34.27
3.5	Coupon	50	0.6435	32.18
4.0	Coupon	50	0.6042	30.21
4.5	Coupon	50	0.5674	28.37
5.0	Coupon	50	0.5327	26.64
5.5	Coupon	50	0.5002	25.01
6.0	Coupon	50	0.4697	23.48
6.5	Coupon	50	0.4410	22.05
7.0	Coupon	50	0.4141	20.71
7.5	Coupon	50	0.3888	19.44
8.0	Coupon	50	0.3651	18.25
8.5	Coupon	50	0.3428	17.14
9.0	Coupon	50	0.3219	16.09
9.5	Coupon	50	0.3022	15.11
10.0	Coupon	50	0.2838	14.19
10.0	Redemption	1,000	0.2838	283.80
PV of Investment	834.72

Price of the bond = 1,213.19 (when required rate of return = 7%) (Note: Since coupon is paid semi-annually, required raturn is converted into per 6-months i.e. 7%/2 = 3.5%)

Year	Type	Cashflow	Present value factor @ 3.5%	Discounted cash flow
0.5	Coupon	50	0.9662	48.31
1.0	Coupon	50	0.9335	46.68
1.5	Coupon	50	0.9019	45.10
2.0	Coupon	50	0.8714	43.57
2.5	Coupon	50	0.8420	42.10
3.0	Coupon	50	0.8135	40.68
3.5	Coupon	50	0.7860	39.30
4.0	Coupon	50	0.7594	37.97
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