FINA1310 2020 Fall Assignment MingZhuTai PDF

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FINA1310E Corporate Finance Semester 1 2020- Assignment 1 Suggested SolutionDue on xx/xx (xxx) at 17:00. No late submission will be accepted. Both typed and hand-written works are acceptable. Please scan your work properly and combine them into one consolidated pdf file. Each group needs to submit o...

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FINA1310 2020 Fall Assignment MingZhuTai FINA1310 2020-2021 2020 Fall Assignment (Group Assignment) From the lecturer MingZhuTai University The University of Hong Kong Course Corporate Finance (FINA1310) Uploaded by Janice Lam Academic year 2020/2021

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Assignment 1 Suggested Solution

Assignment 1.2___

Due on xx/xx (xxx) at 17:00. No late submission will be accepted. Both typed and hand-written works are acceptable. Please scan your work properly and combine them

Assignment 1.3___ into one consolidated pdf file. Each group needs to submit once only. Do not forget to indicate your name, email and UID clearly. Before your submission, you are

Lecture 4suggested - Bond Valuation Chapter 7 and keep it for your own reference. to make a copy of-your finalized work FINA1310 Group KL Assignment 3 Solution with questions Name Email

UID

Member 01

FINA1310 KL Assignment 2 Solution with questions 02 03

Preview text04 05 06

FINA1310E Corporate Finance Semester 1 2020- Assignment 1 Suggested Solution Calculation Questions (200 points)

Due on xx/xx (xxx) at 17:00. No late submission will be accepted. Both typed Please round off all answers to 4 decimal places. and hand-written works are acceptable. Please scan your work properly and 1. Campanula received $50,000 red pocket money from her relatives in the recent Chinese New Year. She invested the whole amount in her bank that offers 7% compound annually interest over a 5-year period. a. Would she have earned more interest if the bank offers 8.5% simple interest over a 5-year period? If so, how much more would she have earned? (5 points) If the bank pays compound interest, by the end of the 5-year period she would get: $50,000 × (1 + 7%), = $70,127.5865 If the bank pays simple interest, by the end of the 5-year period she would get: $50,000 × (1 + 8.5% × 5) = $71,250 Therefore, she would have earned more if the bank pays simple interest. The difference will be

$71,250 − $70,127.5865 = $1,122.4135 b. How about if she invested over a 10-year period? Would she have earned more or less if the bank offers simple interest? And how much more or less would she have earned? (assume the interest rate stays the same) (5 points) If the bank pays compound interest, by the end of the 10-year period she would get: $50,000 × (1 + 7%)56 = $98,357.5679 If the bank pays simple interest, by the end of the 10-year period she would get: $50,000 × (1 + 8.5% × 10 ) = $92,500 Therefore, she would have earned less if the bank pays simple interest. The difference will be

$98,357.5679 − $92,500 = $5857.5679

2. Derek would like to pursue further studies after his undergraduate degree. The postgraduate program that he is considering would cost $330,000 in tuition. Suppose he will receive a $250,000 scholarship 2 year later. In how many years later will he have enough to pursue his further studies if he invests the whole scholarship amount at 8% per annum? (5 points) We solve for 8 in the following equation: $330,000 = $250,000 × (1 + 8% )9 8 = 3.6074 Therefore, in (2 + 3.6 ) = 5.6 years Derek will have enough to pursue his further

studies.

3. Everrich Co. sells you an annuity that pays $3,600 every month from the end of May 2020 to the end of Nov 2023 with annual interest rate 8% compounded monthly. a. What’s the price of this annuity on May 1, 2020? (5 points) PV = $3,600

1−

1 8% (1 + 12 )> 1.8% 5B×B, @1 + 12 A −1 $2,000,000 = C 1.8% 12 C = $5,283.7041

b. Warwick needs to finance his retirement consumption for 15 years after he retired using the $2,000,000 he have at retirement. Thereafter, his son will support his retirement consumption. How much can he consume each month during the 15 years retirement? (assume the interest rate stays the same) (6 points) $2,000,000 = C

1−

1 1.8% 5B×5, (1 + 12 ) 1.8% 12

C = $12,686.8101

5. There are three investments you are considering: Investment 1: Invest in Exceptional Bank that offers a monthly interest rate of 1.4% compounded monthly. Investment 2:

Invest in High Growth Fund that guarantees it will pay 18.2% compounded annually.

Investment 3:

Invest in Super High Return Bank that offers a quarterly interest rate of 4.3% compounded quarterly.

a. What are the APRs for the three investment options? (3 points) Investment 1 APR: 1.4% × 12 = 16.8% Investment 2 APR: 18.2% Investment 3 APR: 4.3% × 4 = 17.2%

b. Which investment options should you choose? (7 points) Investment 1 EAR:

Investment 2 EAR:

Investment 3 EAR:

1 + EAR = (1 + 1.4%)5B EAR = 18.1559% 1 + EAR = (1 + 18.2%)5 EAR = 18.2% 1 + EAR = (1 + 4.3%)< EAR = 18.3415%

Hence we will choose Investment 3.

6. Ryman Healthcare Co. is selling an insurance policy that will make monthly payment of $3,200 for the first 10 years. Thereafter, the insurance policy will start paying $1,800 every month forever. If the interest rate is 7% compounded monthly. What is the value of the insurance policy today? (8 points) Value of annuity: PVA = $3,200

1−

1 7% 5B×56 (1 + 12 ) 7% 12

PVA = $275,604.3333 Value of perpetuity: GHG56 =

$1,800 7% @ 12 A

GHG56 = $308,571.4286 GHG6 =

$308,571.4286 7% 5B×56 @1 + 12 A

GHG6 = $153,543.9911

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1−

(1 +16%), 6%

$360,000 = C C = $85,462.7042

Year

Beginning Principal Balance

Total Payment

Interest Payment

Principal Repayment

1 2 3 4 5

$360,000.00 $296,137.30 $228,442.83 $156,686.70 $80,625.19

$85,462.70 $85,462.70 $85,462.70 $85,462.70 $85,462.70

$21,600.00 $17,768.24 $13,706.57 $9,401.20 $4,837.51

$63,862.70 $67,694.47 $71,756.13 $76,061.50 $80,625.19

Ending Principal Balance $296,137.30 $228,442.83 $156,686.70 $80,625.19 $0.00

> 8. Welch Corporation has two different bonds currently outstanding. Bond WX1 offers 13% coupon. Bond WX2 offers 8% coupon. Both bonds make annual payments, have a YTM of 9%, and have ten years to maturity. a. If interest rates remain unchanged, what are the bond prices this year and 3 years later? (8 points) Bond WX1: P6 = >$130

1−

P= = >$130

1 $1,000 (1 + 9%)56 > = >$J, KLM. NOMP >+> (1 + 9%)56 9%

1−

1 $1,000 (1 + 9%)Q >+> > = >$J, KOJ. PJRJ 9% (1 + 9%)Q

Bond WX2:

1 1 − (1 + 9%)56 $1,000 > = >$SPL. RKPT >+> P6 = >$80 (1 + 9%)56 9% P= = >$80

1−

1 $1,000 (1 + 9%)Q > = >$STS. MNOL >+> (1 + 9%)Q 9%

b. What type of bond WX1 and WX2 are respectively? (i.e. whether it is a Par Bond, Discount Bond or Premium Bond) (2 points)

Bond WX1 is a premium bond. Bond WX2 is a discount bond.

c. Explain the price-time relationship for bond selling at premium or discount based on the previous parts findings, assuming the interest rate remain unchanged (Hint: How the price change across time? And at maturity?) (3 points) The bond prices approaches par as it approaches maturity. Discount bond increase in price. Premium bond decrease in price. d. What are the current yields for the bonds this year? (4 points) Bond WX1: Current>yield> = > Bond WX2: Current>yield> = >

$130 > = >10.3445% $1,256.7063

$80 > = 8.5486% $935.8234

9. You would like to buy a yacht when you retire in 20 years. You are able to save $14,000 in real dollar each year. The nominal return on your saving is 8.65% and the inflation rate is 2.5%. a. What real amount would you have saved to achieve your goal in 20 years? (8 points) (1>+>R)>=>(1>+>r)(1>+>h)> (1 + 8.65%) = (1 + r)(1 + 2.5%) r = 6% >

>

>

(1 + 6%)B6 − 1 FVOA`abc = $14,000 6% FVOA`abc = $LJT, SSR. KNMR

b. What are the values today for the real cash flows? (5 points)

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market expects it can generate 8% return on the common stock. The dividends of the common stock just distributed were $9 per share. a. What is the common stock price today and what is the theoretical common stock price 6 years later? (6 points) D5 P6 = R−g $9>(1 + 3%) 8% − 3% P6 = $JRL. TOOO P6 =

Pm = >$185.4>(1 + 3%)m = $KKJ. PNNP b. Now suppose WaterNet planned to invest in new capital and decided not to

distribute dividends in the next 5 years. The company will distribute a $7.5 per share dividend in 6 years with a growth rate of 3% every year thereafter

and the market expects it can generate 8% return on the common stock. What is the common stock price today? (6 points)> Dm P, = R−g $7.5> 8% − 3% P, = $JLO. OOOO P, =

P6 = >

150 = $JOK. ORNL (1 + 8%),

c. WaterNet also issued preferred shares (constant dividends paid every year forever) with a stated value of $100 each with 5.6% dividends 3 years ago. The next dividend will be paid today and you will receive the next dividend. The required return on the preferred stock is 4%. What is the price of the preferred stock today before the dividend paid today? (6 points) P6 = P6 =

D (1 + R) R

$100> × 5.6% (1 + 4% )> 4%

P6 = $JTL. MOOO

Alternative>way: P6 =

$566>×,.m% >>>>PIg = >>>>>>PIg > = J. KMTM>

$20,000 $30,000 $40,000 $66,000 + + (1 + 12%) + (1 + 12%)B (1 + 12%)= (1 + 12%)< PIÄ = $80,000 PIÄ > = >J. TOKT

d. What is the payback period of each of the project? (6 Points) Payback>Periodg = 2 + ($200,000 − $60,000 − $75,000)⁄$80,000 = K. RJKL>…†‡ˆ‰ Payback>PeriodÄ = 2 + ($80,000 − $20,000 − $30,000) ⁄$40,000 = K. NLOO>…†‡ˆ‰

e. What is the discounted payback period of each of the project? (6 Points) Year 0 1 2 3 4

Cash Flow (A) Discounted CFs (A) Cash Flow (B) Discounted CFs (B) -$200,000 -$200,000 -$80,000 -$80,000 $60,000 $53,571 $20,000 $17,857 $75,000 $59,790 $30,000 $23,916 $80,000 $56,942 $40,000 $28,471 $130,000 $82,617 $66,000 $41,944

Discounted>Payback>Periodg

= 3 + ($200,000 − $170,303) ⁄$82,617 = P. PLSL>…†‡ˆ‰ > Discounted>Payback>PeriodÄ = 3 + ($80,000 − $70,244)⁄$41,944 = P. KPKM>…†‡ˆ‰ >

f. Which project should Sam Sanders Inc. choose based on the above information? (1 points)...