In: Finance
King Solomon is a rich farmer in Tetebia, a town in
the Asou Municipal Assembly. He owns over 100,000 hectares of
farmlands. However, he fears the worst might happen and wants to do
some investments to secure his future and that of his children. He
is contemplating some long term investments he could undertake to
secure his future and that if his children. He is now 50 years old
and he plans to retire in 10 years from active farm work. He
expects to live for another 25 years after he retires –that is,
until age 85. He was advised by a friend that an investment in the
financial market will help him plan his retirement well. He has no
idea about financial markets and how they operate. You recently
graduated and have just reported to work as an investment advisor
at the brokerage firm of Cenden Ltd. King Solomon has approached
your company for advice. Your boss after a discussion with King
Solomon could gather the following information. King Solomon wants
his first retirement payment to have the same purchasing power at
the time he retires as GHȼ 40,000 has today. He wants all of his
subsequent retirement payments to be equal to his first retirement
payment. (Do not let the retirement payments grow with inflation:
King Solomon realizes that the real value of his retirement income
will decline year by year after he retires.) His retirement income
will begin the day he retires, 10 years from today, and he will
then receive 24 additional annual payments. Inflation is expected
to be 5% per year from today forward. He currently has GHȼ 100,000
saved up, and he expects to earn a return on his savings of 8% per
year with annual compounding.
Again, he wants to have a secure university education for his
lovely daughter Daisy. His daughter is now 13 years old. She plans
to enroll at the University of Professional Studies, Accra in 5
years, and it should take her 4 years to complete her education.
Currently, the cost per year (for everything – her food, clothing,
tuition, books, transportation, and so forth) is GH¢ 12,000 per
year. This cost is expected to remain constant throughout the
four-year university education. The daughter recently received GH¢
7,500 from her grandfather’s (King David’s) estate; this money will
be invested at a rate of 8% to help meet the costs of Daisy’s
education. The rest of the costs will be met by money King Solomon
will deposit in a savings account which also earns 8 percent
compound interest per year. He will make 5 equal deposits into the
account, one deposit per annum starting one year from now until his
daughter starts university. These deposits will begin one year from
now. (Assume that school fees are paid at the beginning of the
year).
Again, King Solomon is interested in buying a bond issued by Zenzo
Pharma Ltd. Zenzo Pharma intends to use the proceeds of the bonds
to finance the production of its new vaccine for COVID 19. The bond
has a face value of GH¢10,000 at a coupon rate of 12% and a term to
maturity of 10 years. The bond expects to pay coupons annually.
Included in the bond indenture are call and sinking fund
provisions. The required rate of return on the market for bonds
with similar features is 18% per annum. Your boss had asked you to
advice King Solomon based on the information he provided
Required
a. Explain to King Solomon what financial markets mean and which
three (3) financial instruments he can invest
in.
b. To the nearest cedi, how much must he save during each of the
next 10 years (with equal deposits being made at the end of each
year, beginning a year from today) to meet his retirement goal?
(Note: Neither the amount he saves nor the amount he withdraws
upon
retirement is a growing
annuity.)
c. What will be the present value of the cost of 4 years of
education at the time the daughter
Daisy turns
18?
d. What will be the value of the GH¢ 7,500 that Daisy received from
her grandfather’s estate
when she starts college at
18?
e. If King Solomon is planning to make the first of 5 deposits one
year from now, how large must each deposit be for him to able to
put his daughter through
college?
f. Explain to King Solomon what call provisions and sinking fund
provisions are and how these provisions are expected to affect the
risk of the
bond
g. Which value will you place on a bond of Zenzo Pharma
Ltd?
A) Any marketplace where the trading of securities occurs, including the stock market, bond market, forex market, derivatives market, etc is termed as Financial Market.
When a company is in requireemnet of funds, it can either take a loan or can raise money from Financial Market. In orde to raise money from Financial Market, company has to list its secuirities in Financial Market. These securities can be in form of shares, debentures, etc. If investors wishes to invest in the securities listed by the company, they can purchase the same through Financial market. Now once all the securities of the company has been subscibed to, then Financial Market gives the money to the company and allot the securities to the investors.
Once the securities are alloted to investors, investors then can sell these securities to another investros (either at a higher price to earn a profit, or even at a lower price). These transaction are also done via Financial Market.
Hence, in the financial market, trading of the securities occurs.
Three types of Financial instruement in which King Solomon can invets are shares, bonds, futures. There are many other instruments also in which he can invest, provided he is confortable with the risk and return of that instrument.
B) Todays value = 40,000
Inflation Rate = 5% per year
No of years = 10
Value of 40,000 after 10 years = = 65,155.79
So, his first annual payment will be 65,155.79 and he want to withdraw the same for 24 more years.
Also, he would want to invest x amount every year for 10 years from now. These investments and withdrawls will be done at the end of the year.
Also, he would also earn 8% intrest every year.
Hence, x would be equal to 6229.40. The working of the same is as below -
Year | Opening Balance (A) | Interest @ 8% on Opening Balance (B) | Invest (C) | Withdraw (D) | Closing Balance (A+B+C-D) |
40 | - | 100,000.00 | |||
41 | 100,000.00 | 8,000.00 | 6,229.40 | 114,229.40 | |
42 | 114,229.40 | 9,138.35 | 6,229.40 | 129,597.15 | |
43 | 129,597.15 | 10,367.77 | 6,229.40 | 146,194.32 | |
44 | 146,194.32 | 11,695.55 | 6,229.40 | 164,119.27 | |
45 | 164,119.27 | 13,129.54 | 6,229.40 | 183,478.21 | |
46 | 183,478.21 | 14,678.26 | 6,229.40 | 204,385.87 | |
47 | 204,385.87 | 16,350.87 | 6,229.40 | 226,966.14 | |
48 | 226,966.14 | 18,157.29 | 6,229.40 | 251,352.83 | |
49 | 251,352.83 | 20,108.23 | 6,229.40 | 277,690.46 | |
50 | 277,690.46 | 22,215.24 | 6,229.40 | 306,135.09 | |
51 | 306,135.09 | 24,490.81 | 6,229.40 | 336,855.30 | |
52 | 336,855.30 | 26,948.42 | 6,229.40 | 370,033.12 | |
53 | 370,033.12 | 29,602.65 | 6,229.40 | 405,865.17 | |
54 | 405,865.17 | 32,469.21 | 6,229.40 | 444,563.79 | |
55 | 444,563.79 | 35,565.10 | 6,229.40 | 486,358.29 | |
56 | 486,358.29 | 38,908.66 | 6,229.40 | 531,496.35 | |
57 | 531,496.35 | 42,519.71 | 6,229.40 | 580,245.46 | |
58 | 580,245.46 | 46,419.64 | 6,229.40 | 632,894.50 | |
59 | 632,894.50 | 50,631.56 | 6,229.40 | 689,755.46 | |
60 | 689,755.46 | 55,180.44 | 6,229.40 | 65,155.79 | 686,009.51 |
61 | 686,009.51 | 54,880.76 | 65,155.79 | 675,734.49 | |
62 | 675,734.49 | 54,058.76 | 65,155.79 | 664,637.46 | |
.... | ..... | .... | .... | ... | ... |
80 | 260,148.16 | 20,811.85 | 65,155.79 | 215,804.22 | |
81 | 215,804.22 | 17,264.34 | 65,155.79 | 167,912.78 | |
82 | 167,912.78 | 13,433.02 | 65,155.79 | 116,190.01 | |
83 | 116,190.01 | 9,295.20 | 65,155.79 | 60,329.43 | |
84 | 60,329.43 | 4,826.35 | 65,155.79 | (0.00) |
C) Current per annum cost of university = 12,000. After giving Inflation effect of 5% per annum for 5 years (when she will enroll for university) the cost would be = = 15,315.38
She will take 4 years to complete, and the cost of subequent year will be same, i.e., 15,315.38.
PV of the same 5 years from now (i.e. when Daisy will turn 18 years) is as below (let Re = Inflation Rate = 5%) -
Year | Cost | PV @ 5% | PV |
18 | 15,315.38 | 1.00 | 15,315.38 |
19 | 15,315.38 | 0.95 | 14,586.08 |
20 | 15,315.38 | 0.91 | 13,891.50 |
21 | 15,315.38 | 0.86 | 13,230.00 |
Total | 61,261.52 | 3.72 | 57,022.95 |
Hence, PV of the the cost of 4 years of education at the time Daisy turns 18 is 57,022.95.
Assumptions - 1) Re = Inflation Rate = 5%.
2) Education Cost is to be paid at start of every year. Hence, cost of 1st year is taken as it is only.
D) Value of 7500 5 years from now = = 11019.96
E) Currently Daisy has 7500 from her grandfather. Now, his father will make 5 equal annual deposits in her account (at end of every year) to help her to go through the university. Interest rate will be 8% pa. Hence, per annum, he has to deposit 7459.96. The working of the same is as follows -
Year | Opening Balance (A) | Interest @ 8% on Opening Balance (B) | Invest (C) | Withdraw (D) | Closing Balance (A+B+C-D) |
14 | 7,500.00 | 600.00 | 7,459.96 | 15,559.96 | |
15 | 15,559.96 | 1,244.80 | 7,459.96 | 24,264.73 | |
16 | 24,264.73 | 1,941.18 | 7,459.96 | 33,665.87 | |
17 | 33,665.87 | 2,693.27 | 7,459.96 | 43,819.10 | |
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