The Cost of Fractional Premiums

Saturday, July 25, 2009 11:12
edit
The Cost of Fractional Premiums


I renewed my apartment lease a few weeks ago. After September, my rent will go down — thanks, recession! — from $2,500 to $2,400. I asked my landlord what lump sum he would want if I paid six months of rent (August through January) in July. This is not a typical request from a tenant, so he took a few hours to think about it and came back with an offer of $14,000. That’s $600 or about 4.1% less than the total monthly rent of $14,600 (two months of $2,500 and four months of $2,400).

This Website Is For Financial Professionals Only


By accepting his offer, I’ll have to pay $11,500 in addition to the $2,500 rent that I would otherwise pay for August. What is the annualized rate of return (IRR) on my $11,500 investment?

A. 4.1%

B. 8.2%

C. 17.4%

D. 22.8%

The correct answer is D. The annualized IRR of an outflow of $11,500 followed at monthly intervals by an inflow of $2,500 and four inflows of $2,400 is 22.84%. Said another way, the present value of two monthly payments of $2,500 and four monthly payments of $2,400, discounted at an annualized 22.84%, is $14,000.

This high rate of return will not surprise anyone who is familiar with the cost of fractional premiums; that is, premiums that are paid semi-annually, quarterly or monthly rather than annually. Fractional premiums are also called modal premiums. When you buy a fixed-premium insurance policy — term insurance, traditional whole life, disability income insurance, long-term care insurance — you will probably face a financial decision that is similar to my rent decision. (Flexible-premium insurance policies, such as universal life and variable universal life, also have a choice of premium modes, but the financial decision is different.)

According to 20-year term quotes from Compulife, a $500,000 MetLife policy issued to a 40-year-old female preferred nonsmoker has an annual premium of $469.00, a semi-annual premium of $248.57, a quarterly premium of $126.63, and a monthly premium of $42.22. Here is the cost of each option, expressed in dollars and as an annualized IRR:

 

Modal premium

Total

premiums

Annualized

IRR

Annual

$469.00

$469.00

 

Semi-annual

248.57

497.14

27.2%

Quarterly

126.63

506.52

23.3%

Monthly

42.22

506.64

18.7%

By paying annually rather than semi-annually, you save $28.14 and you earn a 27.2% annualized return on the $220.43 prepayment. By paying annually rather than quarterly, you save $37.52 and you earn a 23.3% return on the $342.37 prepayment. By paying annually rather than monthly, you save $37.64 and you earn an 18.7% return on the $426.78 prepayment.

Here are the costs for the monthly premium mode for a few other companies:

   Annual Premium Monthly Premium   IRR
 Ohio National  $395.00  $35.16  14.7%
 AXA Equitable  415.00  38.07  21.6%
 Ameritas  470.00  41.13  10.8%
 TIAA-CREF  508.05  44.45  10.8%
 Guardian  515.00  44.20  6.5%
 Prudential  515.00  46.35  17.2%

The charges for fractional premiums compensate the insurance company for lost interest, higher administrative costs and higher lapses. A high charge does not necessarily mean a high profit for the company.

From the policyowner’s perspective, the charges are not tax deductible, although they do add to the cost basis and therefore reduce any taxable gain upon surrender.

Another consideration in choosing a premium mode is what happens if you die or discontinue the policy. Is there a refund of any unearned premium? That varies by company and type of policy.

Joseph M. Belth, a retired insurance professor and the editor and publisher of The Insurance Forum, has created a handy online calculator at http://www.theinsuranceforum.com/calc.html. Note, however, that this provides the annual percentage rate (APR), not the internal rate of return (IRR). The APR is a nominal rate that ignores compounding, so it is slightly less than the IRR.

Comments (0)

Write comment

You must be logged in to post a comment. Please register if you do not have an account yet.

busy