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# Multiple Choices Finance Multiple Choice Questions (Multiple Choice Questions Sample)

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Professor

Course

Date

Multiple Choices Finance Questions

1 You are 21 years old and are concerned about your retirement. You want to live comfortably when you retire 49 years from now. Since you wonâ€™t have a house payment (you expect to have the mortgage paid off by then), you figure you will need only $4,000 a month (current dollars) on which to live. You expect inflation to remain at 2.25% for the 49-year period, and you expect $1,850 (current dollars) in social security when you retire at 70 years of age. You expect to live 20 years in retirement. How much do you need to save every month, assuming a 6% annual return on your savings, beginning now?

Remaining time=49 years

Total period of saving=49x12month =588 months

Total amount expected to be used before tax and inflation

=20years x 12months x $4000

=$960000

Considering inflation of 2.25%

Amount =$960000 x 102.25%

=$981600

Less social security after retirement=$981600-$1,850

=$979750

Hence, savings per month=

6% annual return, =94% x $1666.24

=$1567 per month

2 What is the value of a 12-year zero coupon bond, assuming current YTM is 2.95%?

Zero-coupon bonds pay no coupons, but instead pay a par value at maturity

The value of coupon bond, given Yield to Maturity of 2.95%

Use semi-annual compounding:

3 Given information on the following three investments. The first is a preferred stock, redeemed in 15 years at $25 per share, currently selling at $26.57 and has a current annual dividend yield of 7.527%. The second is a common stock trading at $125.32 per share, but pays no dividend now nor is expected to pay one within your 15-year investment horizon. The share price is expected to grow at 8% for 5 years and 4% for ten years, when you are determined to sell the shares. The third investment is a new bond which you can buy at par with a coupon of 7.25%. Assume there are no taxes (!) and that you are risk-neutral. If your discount rate is 3.5%, which has the highest return?

1 First investment

Dividend=7.527%+ additional profit on each share

2 Second investment

Profit per share=25.32% of the total investments

The second investment has the highest return compared to the other two investment plans.

4 What is the value of an account ten years from now, which has an opening balance of $500, to which you contribute $50 per month, and which grows at a 7.5% annualized rate?

Principle amount =opening balance=$500

At the end of first year, contributions=$600

Solution,

P = 500. PMT = 10. r = 7.5/100 = 0.075 (decimal). n = 12. t = 10.

Substituting the figures results in:

Total = [ Compound interest for principal ] + [ Future value of a series ]Total = [ P(1+r/n)^nt ] + [ PMT * (((1 + r/n)^nt - 1) / (r/n)) ]Total = [ 500 (1 + 0.075 / 12) ^ 12(10) ] + [ 50 * (((1 + 0.00625)^120 - 1) / (0.00625)) ]Total = [ 1,056.03 ] + [ 50 * (1.112064 / 0.00625) ]Total = [ 1,056.03 ] + [ 8896.52 ]Total = [ $9,952.55 ]

5 Given the answer in 4, above, if you reinvest the amount into an annuity paid out over four years, how much will your payment be, assuming it carries a guaranteed 4% annualized interest rate, and that it is paid at the beginning of each period?

Solution

P = (((PV) / (1-(1+r)-n)), where P = payment, PV = present value, r = rate per period, n = number of periods. Given that, present value (answer in 4) =$9,952.55, rate per period = 4% and the number of periods = 4 years.

Then, P = (((PV) / (1-(1+r)-n)) = 9,952.55/ (1-(1+4/100)-4 = 9,952.55 / 0.9615 = $10,51.06

6 Note the following cash flows:

Year

PROJECT A

PROJECT B

PROJECT C

PROJECT D

0

-$35,000

-$75,000

-$10,000

-$150,000

1

$0

-$4,350

$0

-$12,500

2

$5,000

-$1,250

$0

-$15,000

3

$7,500

$0

$0

-$20,000

4

$12,500

$5,000

$0

$3,500

5

$12,500

$7,500

$0

$24,000

6

$12,500

$12,500

$0

$30,000

7

$12,500

$20,000

$0

$45,000

8

$12,500

$25,000

$0

$95,000

9

$68,500

$164,500

$60,000

$315,000

As long as the discount rate is a positive value of 12.5%, Project B, C and D will ...

Professor

Course

Date

Multiple Choices Finance Questions

1 You are 21 years old and are concerned about your retirement. You want to live comfortably when you retire 49 years from now. Since you wonâ€™t have a house payment (you expect to have the mortgage paid off by then), you figure you will need only $4,000 a month (current dollars) on which to live. You expect inflation to remain at 2.25% for the 49-year period, and you expect $1,850 (current dollars) in social security when you retire at 70 years of age. You expect to live 20 years in retirement. How much do you need to save every month, assuming a 6% annual return on your savings, beginning now?

Remaining time=49 years

Total period of saving=49x12month =588 months

Total amount expected to be used before tax and inflation

=20years x 12months x $4000

=$960000

Considering inflation of 2.25%

Amount =$960000 x 102.25%

=$981600

Less social security after retirement=$981600-$1,850

=$979750

Hence, savings per month=

6% annual return, =94% x $1666.24

=$1567 per month

2 What is the value of a 12-year zero coupon bond, assuming current YTM is 2.95%?

Zero-coupon bonds pay no coupons, but instead pay a par value at maturity

The value of coupon bond, given Yield to Maturity of 2.95%

Use semi-annual compounding:

3 Given information on the following three investments. The first is a preferred stock, redeemed in 15 years at $25 per share, currently selling at $26.57 and has a current annual dividend yield of 7.527%. The second is a common stock trading at $125.32 per share, but pays no dividend now nor is expected to pay one within your 15-year investment horizon. The share price is expected to grow at 8% for 5 years and 4% for ten years, when you are determined to sell the shares. The third investment is a new bond which you can buy at par with a coupon of 7.25%. Assume there are no taxes (!) and that you are risk-neutral. If your discount rate is 3.5%, which has the highest return?

1 First investment

Dividend=7.527%+ additional profit on each share

2 Second investment

Profit per share=25.32% of the total investments

The second investment has the highest return compared to the other two investment plans.

4 What is the value of an account ten years from now, which has an opening balance of $500, to which you contribute $50 per month, and which grows at a 7.5% annualized rate?

Principle amount =opening balance=$500

At the end of first year, contributions=$600

Solution,

P = 500. PMT = 10. r = 7.5/100 = 0.075 (decimal). n = 12. t = 10.

Substituting the figures results in:

Total = [ Compound interest for principal ] + [ Future value of a series ]Total = [ P(1+r/n)^nt ] + [ PMT * (((1 + r/n)^nt - 1) / (r/n)) ]Total = [ 500 (1 + 0.075 / 12) ^ 12(10) ] + [ 50 * (((1 + 0.00625)^120 - 1) / (0.00625)) ]Total = [ 1,056.03 ] + [ 50 * (1.112064 / 0.00625) ]Total = [ 1,056.03 ] + [ 8896.52 ]Total = [ $9,952.55 ]

5 Given the answer in 4, above, if you reinvest the amount into an annuity paid out over four years, how much will your payment be, assuming it carries a guaranteed 4% annualized interest rate, and that it is paid at the beginning of each period?

Solution

P = (((PV) / (1-(1+r)-n)), where P = payment, PV = present value, r = rate per period, n = number of periods. Given that, present value (answer in 4) =$9,952.55, rate per period = 4% and the number of periods = 4 years.

Then, P = (((PV) / (1-(1+r)-n)) = 9,952.55/ (1-(1+4/100)-4 = 9,952.55 / 0.9615 = $10,51.06

6 Note the following cash flows:

Year

PROJECT A

PROJECT B

PROJECT C

PROJECT D

0

-$35,000

-$75,000

-$10,000

-$150,000

1

$0

-$4,350

$0

-$12,500

2

$5,000

-$1,250

$0

-$15,000

3

$7,500

$0

$0

-$20,000

4

$12,500

$5,000

$0

$3,500

5

$12,500

$7,500

$0

$24,000

6

$12,500

$12,500

$0

$30,000

7

$12,500

$20,000

$0

$45,000

8

$12,500

$25,000

$0

$95,000

9

$68,500

$164,500

$60,000

$315,000

As long as the discount rate is a positive value of 12.5%, Project B, C and D will ...

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