FM for Actuaries

Rates of Return 137
4.19 A 7-year project requires an initial cash injection of $10,000. Expenses of
$500 are incurred at the end of every year. The project starts to generate
income of $3,000 after 3 years, and the income increases at a rate of 10%
every year.
(a) Calculate the yield rate of the project.
(b) Repeat (a), assuming that at the end of each year, the company has to
pay 5% tax on investment income after expenses. (If the net income
in the year is negative, no tax is paid.) Compare your answer with that
obtained in (a).
4.20 On June 1, 2016, an investment account is worth $200. On November 1,
2016, the value has increased to $225 and X is deposited into the account.
On April 1, 2017, the balance becomes $270, and $90 is withdrawn. On June
1, 2017, the account balance is $168. The TWRR of the account is 5%. Find
the DWRR of the account.
4.21 On January 1, an account is worth $70,000. After k months, the balance
increases by 20%, and $4,000 is withdrawn. k +2months prior to the end of
the year, the balance becomes $88,000 and $2,000 is deposited. After 1 year,
the account is worth $80,000. The DWRR of the account is 17.69%.
(a) Find k.
(b) Calculate the TWRR of the account.
4.22 Consider the following table for the cash flows of an investment account:
Time
Fund value
mm/dd/yy Contribution before contribution
01/01/2017 1,000
04/01/2017 –300 500
08/01/2017 +2,000 250
12/31/2017 2,750
(a) Calculate the TWRR and the DWRR of the fund.
(b) Comment on the results.
4.23 The following shows the returns and standard deviations of three stock indices:
US, Germany and Japan: