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Time-value of money

Unit: Financial Management

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August 2025

 1 Questions
Question 2c
     
Assume that you have just won a competition prize with the following options:

Option A:
Lumpsum payment of Sh.25.8 million in 5 years time.
Option B:
A sum of Sh.16 million paid as follows:
  • Sh.5 million payable today.
  • Sh.5.5 million to be paid after one year
  • Sh.5.5 million to be paid after 2 years.
Option C:
Annual payment of Sh.1.4 million for 30 years, the first payment being made at the end of the year.
Option D:
A perpetual payment of Sh.1.38 million.

Required:
Assuming a required rate of return of 8%, advise on the payment option that you would select.
 


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April 2025

 1 Questions
Question 1b
​ ​ ​​Pivot Ltd. is considering raising an additional Sh.20 million to finance an expansion programme. The firm’s existing capital structure which is considered to be optimal is as follows:

Sh.“000”
Ordinary share capital 
100,000
Reserves 
50,000
16% debentures (Sh.1,000 par value) 
62,500
14% preference shares capital (Sh.20 per value)
37,500
250,000

Additional information: 
  1. The firm expects to generate Sh.4 million from retained earnings for this expansion programme. 
  2. Additional new ordinary shares will be issued at Sh.90 each subject to a floatation cost of Sh.10 per share. The most recent dividend paid by the company is Sh.4 per share. The firm’s dividends are expected to grow at the rate of 5% per annum in perpetuity. 
  3. The company will issue new 16% debentures at a price of Sh.1,100 with a floatation cost of Sh.5 per debenture. 
  4. New 14% preference shares will be issued at Sh.30 with a floatation cost of Sh.2 per share. 
  5. Corporation tax rate applicable is 30%. 

Required: 
(i) The cost of retained earnings. 

(ii) The cost of new ordinary share capital. 

(iii) The cost of new 16% debentures.

(iv) The cost of new preference shares. 

(v) The company’s weighted marginal cost of capital (WMCC). 


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April 2024

 1 Questions
Question 4c
​ ​ ​ ​​A company negotiates a Sh.30 million loan for eight years from a financial institution. The interest rate is 14% per annum on the outstanding balance of the loan. The principal and interest will be repaid in eight equal year-end instalments. 

Required: 
(i) Prepare a loan repayment schedule. 

(ii) Determine the amount of interest payable at the end of the 8th year.


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December 2023

 2 Questions
Question 3c
​ ​​An investor plans to borrow a loan of Sh.3 million to purchase a piece of land for his family. The interest rate agreed upon is discounted at a rate of 10% per annum. The loan is repayable in 4 years of equal instalments. 

Required: 
(i) Amount payable per instalment. 

(ii) A loan amortisation schedule.


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Question 3d
​ ​ ​​Jane Kiyo has the following investment options to choose from: 

  • Post Office MIS Scheme, monthly interest 8% per annum. 
  • ICD Bank Deposit, quarterly interest 8.25% per annum. 
  • HDFC Ltd., half-yearly interest 8.50% per annum. 
Required: 
Using effective interest rate (EIR) method, advise Jane Kiyo on the preferred investment option.


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August 2023

 1 Questions
Question 5b
​ ​​Joel Ouma needs Sh.9,000,000 in five years’ time to purchase a house. He is determined to deposit a given amount of money each quarter in a sinking fund that earns interest at the rate of 12% compounded quarterly for five years. 

Required: 
Compute the amount of money that Joel Ouma should deposit in each quarter in a sinking fund so as to enable him realise Sh.9,000,000 in five years time.


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April 2023

 1 Questions
Question 5d
​​John Osoro has deposited Sh.700,000 into a savings account at an annual interest rate of 5% compounded monthly with additional deposits of Sh.10,000 per month (made at the end of each month). 

Required: 
Determine the value of the investment after 10 years.


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December 2022

 1 Questions
Question 1c
​​Your client, Alfred Otieno, wishes to invest Sh.500,000 for two years (with interest compounded) but with the right to withdraw at a moment’s notice. The following investment options are available: 
 
Option I: Invest with Nyumba Building Society currently offering an interest rate of 14% per annum after tax with interest paid half yearly. 
 
Option II: Invest with Kijiji Bank Ltd. at an interest rate of 17% per annum with interest paid annually. 
 
Option III: Invest with Faida Bank Ltd. which is offering 16% per annum, interest paid every three months.  
 
Required: 
(i) Using suitable computations, advise your client on the best investment option he should consider. 
 
(ii) Calculate the effective rate of interest for option I. 
 
(iii) Identify TWO situations that could affect your recommendation in (c) (i) above.


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August 2022

 1 Questions
Question 4c
​​Digital Ltd. has some computer industrial plant which it intends to replace four years from today. The company’s director estimates that the cost of the plant to the company at that time will be Sh.30 million. To finance the operations, the Finance Director has decided to set up a fund with Golden Bank Ltd. Golden Bank Ltd. has assured the Finance Director that if he opts for this option, the rate of interest will be fixed at 8% per annum. The Finance Director intends to set aside a constant amount from his annual budgets to finance the plant. The rate of interest will be compounded semi-annually. 

Required: 
The amount that the Finance Director should deposit with Golden Bank Ltd. every year to achieve his objective.


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April 2022

 1 Questions
Question 2a
​ ​James Chege intends to accumulate Sh.10,000,000 in his bank account 15 years from now.

Required:
The amount he should deposit now assuming that the bank is offering a 5% interest rate per annum compounded semi-annually. 


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Pilot December 2021

 1 Questions
Question 4a
​​Jade Smith will deposit Sh.500,000 in his savings account on 31 December 2021. He will deposit an additional Sh.200,000 at the end of each subsequent year in that account, the sum deposited is expected to earn interest at the rate of 8% per annum, compounded annually. 

Required: 
(i) Determine the cumulative amount that is expected to be in his account at the end of year 2025. 

(ii) The rate of return expected to be earned over the projected period.


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December 2021

 1 Questions
Question 3b
​​Siphony Ltd. borrowed Sh.15,000,000 from Baraka Bank at an annual interest rate of 16% repayable in four equal annual instalments at the end of each year. 

Required: 
Prepare a loan amortisation schedule for the company.


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September 2021

 1 Questions
Question 1a
​​The concept of time value of money lays a solid foundation upon which other finance concepts are developed. 

In light of the above statement, explain three applications of the concept of time vafue of money.


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