TVM

Question 1

For an investment that provides a 1.25% return quarterly, its effective annual rate is:

Answer 1

CIMA Section I.B.1. Time Value of Money

From the CIMA Formula Sheet for Effective Annual Return,

EAR = [1 + (Rnom/n)]n -1 = [1 + (0.0125)]4 -1 = 1.0509 - 1 = 0.0509 = 5.09%

Note that the periodic (i.e., quarterly) return represented by Rnom/n has already been provided as 1.25%).

Question 2

A bank proudly advertises that it only charges customers 12.5% interest. Interest is compounded monthly. What is the effective annual rate of this program?

Answer 2

From the CIMA Formula Sheet for Effective Annual Return,

EAR = [1 + (Rnom/n)]n -1 = [1 + (0.125/12)]12 - 1 = [1.04167] 12 - 1 = 1.1324 – 1 = 0.1324 = 13.24%

Question 3

Bobby Thompson is considering buying a real estate property that would generate the following cash flows: year 1 = +45,000, year 2 = +75,000, year 3 = +$110,000, year 4 = $130,000. Bobby believes he can sell it after 4 years for $2,500,000. Bobby’s required rate of return for a project like this is 9% per year. After crunching the numbers you tell Bobby the following:

Answer 3

Don’t pay more than $2,052,509 for the investment.

Enter the initial investment in year 0 as $0;

enter the following cash flows for years 1 through 4: $45,000, $75,000, $110,000, and $2,630,000.

Enter 9% for “i”.

Solve for NPV which is $2.0525 million.

Bobby should not pay more than this amount to achieve his required rate of return.

Question 4

Sean and Susan are methodical savers and you’ve worked with them for exactly 10 years now. When you met them, they already had $400,000 saved for retirement. They turned that account over to you to manage. Additionally, they invested another $50,000 a year over the last decade and just made a large contribution of $150,000 in the account as well. Despite the highly volatile market and given your talents and your ability to manage yours and your client’s emotions during bear markets, the account returned 9.7% net of fees and expenses. Inflation was a modest 2.2% over that same period.

What is the value of the account today after adjusting for the impact of inflation?

Answer 4

$1,664,241

Using a financial calculator….

PV = -$400,000
PMT = -$50,000
“i” or “r” = 7.34% ((1.097/1.022)-1)N = 10 (years)
Solve for FV…. = $1,514,240 + $150,000 contribution at end of year 10.