Question Tag: Discounting

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QTB – Nov 2015 – L1 – SA – Q18 – Mathematics of Business Finance

This question identifies the term used to describe the process of calculating present value from future value.

The term used to describe the process of working backwards in time to find the present value from the future value of an investment is known as:

A. Discount
B. Discounting
C. Discount Rate
D. Annuity
E. Amortization

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BMF – Nov 2023 – L1 – SA – Q5 – Investment Decisions

Calculate the present value of a future amount discounted at 12%.

Calculate the present value, discounted at 12 percent, of receiving N300,000 at the end of year 6.

A. 151,989.34
B. 162,999.34
C. 173,989.34
D. 184,989.34
E. 195,989.34

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BM – May 2024 – L1 – SA – Q17 – Basics of Business Finance and Financial Markets

Calculating the present value of receiving a fixed amount of money discounted at a specific rate.

Calculate the present value, discounted at 15 percent, of receiving ₦500,000 at the end of year 4.
A. ₦245,836.22
B. ₦255,846.32
C. ₦265,856.42
D. ₦275,866.52
E. ₦285,876.62

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QT – May 2019 – L1 – Q2b – Mathematics of Business Finance

Calculate NPV and IRR for two machines and determine which machine yields a better return.

BonBone Company Ltd wants to make a decision on which of the two machines to purchase. Each will involve a GH¢10,000 investment. The expected net incremental cash flows are given by the table below:

Year Machine I (GH¢) Machine II (GH¢)
1 5,000.00 2,000.00
2 4,000.00 3,000.00
3 2,000.00 5,000.00
4 2,000.00 4,000.00

Required:

i) If the company’s cost of capital is 10%, calculate the Net Present Value (NPV) of Machine I and Machine II and determine which machine should be purchased for higher returns. (8 marks)

ii) If the initial investment for Machine I is changed to GH¢4,000 and Machine II is changed to GH¢2,000, calculate the Internal Rate of Return (IRR) for Machine I and Machine II. (6 marks)

iii) If the IRRs in (ii) above are to be used as the basis of selection, determine which machine should be purchased for higher returns. (2 marks)

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QT – May 2019 – L1 – Q2a – Mathematics of Business Finance

Distinguish between IRR and NPV, and evaluate investment decisions using NPV and IRR.

Distinguish between Internal Rate of Return and Net Present Value. (4 marks)

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QT – May 2017 – L1 – Q2b – Mathematics of Business Finance

Determine the present value of future sums and identify the preferred business opportunity.

A model for calculating the amount required, , to achieve a specified sum at some future point in time,  years at a rate of interest r, is given by:

Required:

i) Determine the present value of GH¢7000.00 payable in 4 years.
(7 marks)

ii) Determine the present value of GH¢8000.00 payable in 6 years.
(7 marks)

You are required to discount these future sums using an interest rate of 8%.

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QT – Nov 2018 – L1 – Q3a – Mathematics of Business Finance

Determine how much to invest at 6% per annum to earn an annual income of GH¢15,000 for 10 years.

Kwabena was able to recover GH¢150,000 out of GH¢200,000 invested in the Savings and Loans Company. How much money should he invest at a return of 6% per annum so as to earn an annual income of GH¢15,000 for a period of 10 years? (10 marks)

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AFM – May 2019 – L3 – Q2a – Discounted cash flow techniques

Compare leasing and buying options for a machine and recommend the most viable choice based on net present value analysis.

Rahim Ltd requires a machine for 5 years. There are two alternatives, either to take it on lease or buy basis. The company is reluctant to invest an initial amount for the project and approaches their bankers. The bankers are ready to finance 100% of its initial required amount at a 15% rate of interest for any of the alternatives.

Under lease option, an upfront security deposit of GH¢5,000,000 is payable to the lessor, which is equal to the cost of the machine. Out of which, 40% shall be adjusted equally against annual lease rent. At the end of life of the machine, the expected scrap value will be at book value after providing depreciation at 20% on written down value basis.

Under the buying option, loan repayment is in equal annual installments of the principal amount, which is equal to annual lease rent charges. However, in the case of bank finance for the lease option, repayment of principal amount equal to lease rent is adjusted every year, and the balance at the end of 5th year.

Assume income tax rate is 30%, interest is payable at the end of every year, and discount rate at 15% p.a. The following discounting factors are given:

Year Factor
1 0.8696
2 0.7562
3 0.6576
4 0.5718
5 0.4972

Required:
Recommend the most viable option on the basis of net present values.

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CR – Nov 2018 – L3 – Q2b – Financial instruments: Recognition and measurement Corporate reporting

Recommend the financial reporting treatment for an interest-free government loan received by Bole Bamboi Ltd, including suitable calculations.

On 1 June 2017, Bole Bamboi Ltd (Bole Bamboi) purchased a factory building in a regional development area for GH¢4 million. It used the building to store some relocated equipment, but shortly after the purchase, the roof needed to be replaced. Bole Bamboi has been replacing the roof of the factory building with an environmentally friendly one, including insulation and integrated solar panels. The replacement of the roof will cost GH¢2 million. The cost of the replacement is to be incurred by Bole Bamboi; however, the Ministry of Trade and Industry advanced a 5-year, interest-free loan to Bole Bamboi on 1 July 2017 to finance the GH¢2 million cost. The loan has to be repaid in 5 equal annual instalments of GH¢400,000 beginning on 30 June 2018. An equivalent loan from Bole Bamboi’s bank with the same repayment terms would have been made at a fixed annual interest rate of 5% for the 5 years.

The present value of 5 annual payments of GH¢1 at 5% is GH¢4.32948.

Required:
In accordance with IFRS, recommend, with suitable calculations, the financial reporting treatment of the above items in the financial statements of Bole Bamboi for the year ended 31 December 2017.

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QTB – Nov 2015 – L1 – SA – Q18 – Mathematics of Business Finance

This question identifies the term used to describe the process of calculating present value from future value.

The term used to describe the process of working backwards in time to find the present value from the future value of an investment is known as:

A. Discount
B. Discounting
C. Discount Rate
D. Annuity
E. Amortization

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BMF – Nov 2023 – L1 – SA – Q5 – Investment Decisions

Calculate the present value of a future amount discounted at 12%.

Calculate the present value, discounted at 12 percent, of receiving N300,000 at the end of year 6.

A. 151,989.34
B. 162,999.34
C. 173,989.34
D. 184,989.34
E. 195,989.34

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BM – May 2024 – L1 – SA – Q17 – Basics of Business Finance and Financial Markets

Calculating the present value of receiving a fixed amount of money discounted at a specific rate.

Calculate the present value, discounted at 15 percent, of receiving ₦500,000 at the end of year 4.
A. ₦245,836.22
B. ₦255,846.32
C. ₦265,856.42
D. ₦275,866.52
E. ₦285,876.62

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QT – May 2019 – L1 – Q2b – Mathematics of Business Finance

Calculate NPV and IRR for two machines and determine which machine yields a better return.

BonBone Company Ltd wants to make a decision on which of the two machines to purchase. Each will involve a GH¢10,000 investment. The expected net incremental cash flows are given by the table below:

Year Machine I (GH¢) Machine II (GH¢)
1 5,000.00 2,000.00
2 4,000.00 3,000.00
3 2,000.00 5,000.00
4 2,000.00 4,000.00

Required:

i) If the company’s cost of capital is 10%, calculate the Net Present Value (NPV) of Machine I and Machine II and determine which machine should be purchased for higher returns. (8 marks)

ii) If the initial investment for Machine I is changed to GH¢4,000 and Machine II is changed to GH¢2,000, calculate the Internal Rate of Return (IRR) for Machine I and Machine II. (6 marks)

iii) If the IRRs in (ii) above are to be used as the basis of selection, determine which machine should be purchased for higher returns. (2 marks)

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QT – May 2019 – L1 – Q2a – Mathematics of Business Finance

Distinguish between IRR and NPV, and evaluate investment decisions using NPV and IRR.

Distinguish between Internal Rate of Return and Net Present Value. (4 marks)

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QT – May 2017 – L1 – Q2b – Mathematics of Business Finance

Determine the present value of future sums and identify the preferred business opportunity.

A model for calculating the amount required, , to achieve a specified sum at some future point in time,  years at a rate of interest r, is given by:

Required:

i) Determine the present value of GH¢7000.00 payable in 4 years.
(7 marks)

ii) Determine the present value of GH¢8000.00 payable in 6 years.
(7 marks)

You are required to discount these future sums using an interest rate of 8%.

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QT – Nov 2018 – L1 – Q3a – Mathematics of Business Finance

Determine how much to invest at 6% per annum to earn an annual income of GH¢15,000 for 10 years.

Kwabena was able to recover GH¢150,000 out of GH¢200,000 invested in the Savings and Loans Company. How much money should he invest at a return of 6% per annum so as to earn an annual income of GH¢15,000 for a period of 10 years? (10 marks)

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AFM – May 2019 – L3 – Q2a – Discounted cash flow techniques

Compare leasing and buying options for a machine and recommend the most viable choice based on net present value analysis.

Rahim Ltd requires a machine for 5 years. There are two alternatives, either to take it on lease or buy basis. The company is reluctant to invest an initial amount for the project and approaches their bankers. The bankers are ready to finance 100% of its initial required amount at a 15% rate of interest for any of the alternatives.

Under lease option, an upfront security deposit of GH¢5,000,000 is payable to the lessor, which is equal to the cost of the machine. Out of which, 40% shall be adjusted equally against annual lease rent. At the end of life of the machine, the expected scrap value will be at book value after providing depreciation at 20% on written down value basis.

Under the buying option, loan repayment is in equal annual installments of the principal amount, which is equal to annual lease rent charges. However, in the case of bank finance for the lease option, repayment of principal amount equal to lease rent is adjusted every year, and the balance at the end of 5th year.

Assume income tax rate is 30%, interest is payable at the end of every year, and discount rate at 15% p.a. The following discounting factors are given:

Year Factor
1 0.8696
2 0.7562
3 0.6576
4 0.5718
5 0.4972

Required:
Recommend the most viable option on the basis of net present values.

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CR – Nov 2018 – L3 – Q2b – Financial instruments: Recognition and measurement Corporate reporting

Recommend the financial reporting treatment for an interest-free government loan received by Bole Bamboi Ltd, including suitable calculations.

On 1 June 2017, Bole Bamboi Ltd (Bole Bamboi) purchased a factory building in a regional development area for GH¢4 million. It used the building to store some relocated equipment, but shortly after the purchase, the roof needed to be replaced. Bole Bamboi has been replacing the roof of the factory building with an environmentally friendly one, including insulation and integrated solar panels. The replacement of the roof will cost GH¢2 million. The cost of the replacement is to be incurred by Bole Bamboi; however, the Ministry of Trade and Industry advanced a 5-year, interest-free loan to Bole Bamboi on 1 July 2017 to finance the GH¢2 million cost. The loan has to be repaid in 5 equal annual instalments of GH¢400,000 beginning on 30 June 2018. An equivalent loan from Bole Bamboi’s bank with the same repayment terms would have been made at a fixed annual interest rate of 5% for the 5 years.

The present value of 5 annual payments of GH¢1 at 5% is GH¢4.32948.

Required:
In accordance with IFRS, recommend, with suitable calculations, the financial reporting treatment of the above items in the financial statements of Bole Bamboi for the year ended 31 December 2017.

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