1) Analysts predict that your company\'s earnings will grow at 40% per year for

Question

1) Analysts predict that your company's earnings will grow at 40% per year for the next five years. After that, earnings growth is expected to slow to 2% per year and continue at that level forever. Your company has announced earnings of $2 million. What is the Present Value of all future earnings if the interest rate is 10%? (Assume all cash flows occur at the end of the year.)

2) The house costs $200,000. You have $29,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 8% per year. What will your annual payment be if you sign up for this mortgage?

3) You decice you need to save $2,000,000 by the time you are 65. Today is your 30th birthday and you decide starting today, and continuing on every birthday including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 7%, the amount you deposite each year to make sure that you will have $2,000,000 in the account on your 65th birthday?

4) You have an investment opportunity that requires an initial investment of $9,500 today and will pay $9,000 in one year. What is the IRR of this opportunity?

Explanation / Answer

1.

This problem consists of two parts:
(1) A growing annuity for 5 years;
(2) A growing perpetuity after 5 years.
First we find the PV of (1):

= 2.6/(0.1-0.3) * (1-(1.3/1.1)^5) = $16.97 million

Now we calculate the PV of (2). The value at date 5 of the growing perpetuity is

= (2.6)^5 * (1.02)/0.1-0.02 = $ 94.68 million.

PV = 94.68/(1.1)^5 = $ 58.79 million

Adding them we get = 16.97 + 58.79 = $75.76 million

2.

3.

FV = $2 million
The PV of the cash flows must equal the PV of $2 million in 35 years. The cash flows consist of a 35-year annuity, plus the contribution today, so the PV is:

c/.07 * ( 1-1/(1.07)^35) + c

The PV of $2 million in 35 years is

2,000,000/(1.07)^35 = 187,325.88

c = 187,325.88 / 1/1.07 * ( 1 - (1/1.07)^35)+1

= 13,430.62

4) The IRR would be -5%.

Year Month Beginning Balance Payment Principal Interest Cumulative Principal Cumulative Interest Ending Balance 2015 Jan 171,000.00 1,254.74 114.74 1,140.00 114.74 1,140.00 170,885.26 Feb 170,885.26 1,254.74 115.50 1,139.24 230.24 2,279.24 170,769.76 Mar 170,769.76 1,254.74 116.27 1,138.47 346.51 3,417.71 170,653.49 Apr 170,653.49 1,254.74 117.05 1,137.69 463.56 4,555.40 170,536.44 May 170,536.44 1,254.74 117.83 1,136.91 581.39 5,692.31 170,418.61 Jun 170,418.61 1,254.74 118.62 1,136.12 700.01 6,828.43 170,299.99 Jul 170,299.99 1,254.74 119.41 1,135.33 819.42 7,963.76 170,180.58 Aug 170,180.58 1,254.74 120.20 1,134.54 939.62 9,098.30 170,060.38 Sep 170,060.38 1,254.74 121.00 1,133.74 1,060.62 10,232.04 169,939.38 Oct 169,939.38 1,254.74 121.81 1,132.93 1,182.43 11,364.97 169,817.57 Nov 169,817.57 1,254.74 122.62 1,132.12 1,305.05 12,497.09 169,694.95 Dec 169,694.95 1,254.74 123.44 1,131.30 1,428.49 13,628.39 169,571.51 Yearly Schedule of Balances and Payments Year Beginning Balance Payment Principal Interest Cumulative Principal Cumulative Interest Ending Balance 2016 169,571.51 15,056.88 1,546.67 13,510.21 2,975.16 27,138.60 168,024.84 2017 168,024.84 15,056.88 1,675.44 13,381.44 4,650.60 40,520.04 166,349.40 2018 166,349.40 15,056.88 1,814.50 13,242.38 6,465.11 53,762.41 164,534.89 2019 164,534.89 15,056.88 1,965.11 13,091.77 8,430.21 66,854.19 162,569.79 2020 162,569.79 15,056.88 2,128.21 12,928.67 10,558.42 79,782.86 160,441.58 2021 160,441.58 15,056.88 2,304.85 12,752.03 12,863.27 92,534.89 158,136.73 2022 158,136.73 15,056.88 2,496.15 12,560.73 15,359.42 105,095.62 155,640.58 2023 155,640.58 15,056.88 2,703.33 12,353.55 18,062.74 117,449.18 152,937.26 2024 152,937.26 15,056.88 2,927.70 12,129.18 20,990.45 129,578.35 150,009.55 2025 150,009.55 15,056.88 3,170.70 11,886.18 24,161.15 141,464.53 146,838.85 2026 146,838.85 15,056.88 3,433.87 11,623.01 27,595.02 153,087.54 143,404.98 2027 143,404.98 15,056.88 3,718.88 11,338.00 31,313.89 164,425.55 139,686.11 2028 139,686.11 15,056.88 4,027.54 11,029.34 35,341.44 175,454.88 135,658.56 2029 135,658.56 15,056.88 4,361.83 10,695.05 39,703.26 186,149.94 131,296.74 2030 131,296.74 15,056.88 4,723.86 10,333.02 44,427.12 196,482.96 126,572.88 2031 126,572.88 15,056.88 5,115.93 9,940.95 49,543.05 206,423.91 121,456.95 2032 121,456.95 15,056.88 5,540.55 9,516.33 55,083.61 215,940.23 115,916.39 2033 115,916.39 15,056.88 6,000.42 9,056.46 61,084.02 224,996.70 109,915.98 2034 109,915.98 15,056.88 6,498.45 8,558.43 67,582.47 233,555.13 103,417.53 2035 $103,417.53 $15,056.88 $7,037.82 $8,019.06 $74,620.29 $241,574.19 $96,379.71 2036 $96,379.71 $15,056.88 $7,621.95 $7,434.93 $82,242.24 $249,009.12 $88,757.76 2037 $88,757.76 $15,056.88 $8,254.57 $6,802.31 $90,496.81 $255,811.43 $80,503.19 2038 $80,503.19 $15,056.88 $8,939.69 $6,117.19 $99,436.50 $261,928.62 $71,563.50 2039 $71,563.50 $15,056.88 $9,681.69 $5,375.19 $109,118.19 $267,303.81 $61,881.81 2040 $61,881.81 $15,056.88 $10,485.26 $4,571.62 $119,603.45 $271,875.43 $51,396.55 2041 $51,396.55 $15,056.88 $11,355.53 $3,701.35 $130,958.98 $275,576.78 $40,041.02 2042 $40,041.02 $15,056.88 $12,298.04 $2,758.84 $143,257.02 $278,335.62 $27,742.98 2043 $27,742.98 $15,056.88 $13,318.77 $1,738.11 $156,575.78 $280,073.74 $14,424.22 2044 $14,424.22 $15,056.88 $14,424.22 $632.66 $171,000.00 $280,706.40 $0.00

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