Life Insurance Needs To Replace Income

A little confused as to when we can use a more simple appoach and when we need to break out specific cash flows.

Schweser Practice Problem:
At a subsequent meeting, Westin asks Hyde whether it makes financial sense to continue a temporary $1,500,000 life insurance policy he took out a few years ago. It is a term policy with a guaranteed annual renewal for the next eight years, but at an increasing premium. Westin and Hyde discuss the issue and agree to make certain assumptions. Westin wants to replace his current before tax salary of $200,000 for five years. The salary is paid at the end of the year and will increase by 3% a year thereafter. Given the risky nature of the business, an 11% discount rate is suitable. There are no tax issues to consider and no financial penalties if the current insurance policy is canceled.

C. Based on Westin and Hyde’s assumptions, calculate the amount of insurance Westin would need to replace pretax salary. Show your calculations. State and justify based on Westin’s situation whether Hyde should recommend Westin continue or discontinue having life insurance. Do not use the calculation amount as a justification. Assume Westin could continue the existing policy or take out a new policy for any desired amount.

Schweser Answer:

Year Salary PY @ 11% discount rate
1 $200,000.00 $180,180.18
2 $206,000.00 $167,194.22
3 $212,180.00 $155,144.19
4 $218,545.40 $143,962.62
5 $225,101.76 $133,586.94
Insurance need:** $780,068.15

Discontinue life insurance: Westin has substantial other liquid assets that could provide for his children if he dies prematurely.

Candidate discussion:

2 points for showing the calculation process and 1 point for $780,068. The case facts are specific as to the timing of the flows so other solutions are not accepted in this case.

Why can’t we simply use (1.11/1.03) -1 = 7.766% and then plug that into our financial calculator to get I/Y: 7.766% PMT: $200K N=5 CPT = CPT PV: $803,470 I’ve seen this method used in many other similar problems, but having a hard time understanding when to use which method?

Try PMT = 200,000/1.03 = 194,174.757 and I = 7.76699029. :+1: :nerd_face:

What’s the rationale? Thanks for the reply!

Since you are using an immediate annuity, the PV is at time 0, while the first payment occurs at time 1. To project out the payments correctly, you need to start with 194,174.757 at time 0 in order to project a payment of 200,000 at time 1. You could also use BGN mode with PMT =200,000, but then you would have to discount that PV by one year’s interest @ 11%.

The CF worksheet would also work fine for this problem.

Thanks for your help. Much appreciated.

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