Question

1. Mark decided to save R5 every time his parents get paid and give him pocket money. His parents get paid at the beginning of every second week and give pocket money to each of their children immediately. Mark would earn 3% per week on his funds. If Mark commits to set aside the funds for 2.5 years, How much will Mark receive at the end of the 2.5 years?

2. Shopeasy's earnings and dividends have been growing at a rate of 17% per annum. This growth rate is expected to continue for 6 years (2020 to 2025). After that the growth rate will decrease to 10% for the subsequent 5 years until 2030. Thereafter the growth rate is expected to be consistent at 3.5% forever. If the last dividend per share was R123 and the investors required rate of return on Shopeasy's equity is 9%.

Required : Compute the current value per share from 2026 to 2030

3.

ABC's earnings and dividends have been growing at a rate of 7% per annum. This growth rate is expected to continue for 6 years (2020 to 2025). After that the growth rate will increase to 10% for the subsequent 5 years until 2030. Thereafter the growth rate is expected to be consistent at 2% forever. If the last dividend per share was R70 and the investors required rate of return on ABC's equity is 9%.

Required : Compute the current value per share of ABC if the growth rate is estimated to be 7% from 2020 to 2031 and beyond(forever)

Answer 1

1) Saving = 5 | Rate = 3% per week | Time = 2.5 years

As he gets pocket money at the beginning of every second week, that means he gets paid every week but at the end of the period. Hence, we can use future value of annuity formula for calculation of amount at the end of 2.5 years.

Rate is already in per week basis. Time = 2.5 years or 2.5 * 52 = 130 weeks

FV of Annuity = (PMT/R) * ((1 + R)^N - 1)

Amount at the end of 2.5 years = (5/3%)*((1+3%)¹³⁰ - 1) = 7,608.11

2) Div Year 0 = 123 | Growth for first 6 years = 17% | Growth for next 5 years = 10% | Growth thereafter = 3.5%

Cost of equity = 9%

Since required is to calculate current value of share for cashflow period from 2026 to 2030.

First, let's find out Dividend at Year 2025 using 17% growth rate, that is at the end of 6th Year.

Dividend at 6th Year = 123 * (1+17%)⁶ = 315.52

Now since we need to find the Current value for 2026 to 2030, we will use PV of Growing Annuity formula, where 315.52 will be the payment, 10% will be the growth rate and 9% will be the Rate of return.

PV of Growing Annuity = (PMT / (R - G))*(1-((1+G)/(1+R))^N)

Current Value per share from 2026 to 2030 = (315.52/(9%-10%))*(1-((1+10%)/(1+9%))⁵)

Current Value per share from 2026 to 2030 = 1,474.12

3) Since required is to calculate current value per share from 2020 to 2031 at an estimated growth rate of 7% for period between 2020 to 2031 and forever, hence, it becomes a growing perpetuity with a growth of 7%.

As Dividend at Year 0 = 70 (Remaining data on growth rate becomes irrelevant since required part has given one growth rate for the period)

PV of Growth Perpetuity = PMT*(1+G) / (R - G)

Rate of return, R = 9% | Growth, G = 7% | PMT or Dividend = 70

Current Value of share = 70 * (1+7%) / (9% - 7%)

Current value of share = 74.9 / 2%

Current Value of share of ABC at growth of 7% = 3,745