Question

Q1

a) If higher leverage is associated with greater risk, explain why the process of deleveraging (reducing leverage) can be destabilizing.

b)

You wish to buy an annuity that makes monthly payments for as long as you live. Describe what happens to the purchase price of the annuity if:

(1) your age at the time of purchase goes up, (10 points)

(2) the size of the monthly payment rises, and (10 points)

(3) your health improves. (10 points)

Answer 1

Q1 (a): Higher leverage is indeed associated with higher risk because it creates solvency issues. Higher the leverage, higher the solvency ratios, which means the company does not enjoy investors’ confidence in the business and forgoes the benefits related to capital raised via equity which is reinvesting the profits back into the business without the burden of compulsory payments. However, having said that, debt also brings with it certain benefits, the first and the foremost being lower taxes (taxes saved due to paying interest on debt) and reducing the burden on weighted average cost of capital (WACC). WACC is a function of cost of Equity (Ke) plus cost of Debt (Kd).

Now, as we all know that debt is relatively cheaper as compared to capital because it entails fixed payments which is not the case with Equity. Accordingly, any instrument with fixed payments will naturally be less riskier as compared to instrument with no fixed payments (like shares). Raising debts helps in increasing return on Equity, so in order to achieve an optimum WACC, a company should aim for a proper mix of debt and capital. Going total equity will reduce Return on Equity (RoE). Once RoE increases, valuations go down for the company and once valuations go down, it clicks panic button. So, deleveraging is not the solution.

Q1 (b): The price decreases as you age, Let's take below excel sheet summary, suppose you expect (by estimating your own death) 90 annuity payments and your required rate of return is 7% and the annuity will pay $15 each month, then the price will come to $1048 (refer to pic 1) but let's just suppose in another screenshot that you have aged and now only expect 60 annuity payments until your death, then you will only pay $757 (refer to pic 2)

PIC 1

1	15	14.91301
2	15	14.82653
3	15	14.74055
4	15	14.65506
5	15	14.57008
6	15	14.48558
7	15	14.40158
8	15	14.31806
9	15	14.23503
10	15	14.15248
11	15	14.0704
12	15	13.98881
13	15	13.90768
14	15	13.82703
15	15	13.74685
16	15	13.66713
17	15	13.58787
18	15	13.50907
19	15	13.43073
20	15	13.35284
21	15	13.2754
22	15	13.19842
23	15	13.12188
24	15	13.04578
25	15	12.97013
26	15	12.89491
27	15	12.82013
28	15	12.74579
29	15	12.67187
30	15	12.59838
31	15	12.52532
32	15	12.45269
33	15	12.38047
34	15	12.30868
35	15	12.2373
36	15	12.16633
37	15	12.09577
38	15	12.02563
39	15	11.95589
40	15	11.88656
41	15	11.81762
42	15	11.74909
43	15	11.68096
44	15	11.61322
45	15	11.54587
46	15	11.47891
47	15	11.41235
48	15	11.34616
49	15	11.28036
50	15	11.21495
51	15	11.14991
52	15	11.08525
53	15	11.02096
54	15	10.95705
55	15	10.89351
56	15	10.83034
57	15	10.76753
58	15	10.70509
59	15	10.64301
60	15	10.58129
61	15	10.51992
62	15	10.45892
63	15	10.39826
64	15	10.33796
65	15	10.27801
66	15	10.21841
67	15	10.15915
68	15	10.10023
69	15	10.04166
70	15	9.983427
71	15	9.925531
72	15	9.867972
73	15	9.810746
74	15	9.753851
75	15	9.697287
76	15	9.641051
77	15	9.585141
78	15	9.529555
79	15	9.474291
80	15	9.419348
81	15	9.364724
82	15	9.310416
83	15	9.256423
84	15	9.202744
85	15	9.149375
86	15	9.096317
87	15	9.043565
88	15	8.99112
89	15	8.938979
90	15	8.887141
		1047.979

PIC 2

1	15	14.91301
2	15	14.82653
3	15	14.74055
4	15	14.65506
5	15	14.57008
6	15	14.48558
7	15	14.40158
8	15	14.31806
9	15	14.23503
10	15	14.15248
11	15	14.0704
12	15	13.98881
13	15	13.90768
14	15	13.82703
15	15	13.74685
16	15	13.66713
17	15	13.58787
18	15	13.50907
19	15	13.43073
20	15	13.35284
21	15	13.2754
22	15	13.19842
23	15	13.12188
24	15	13.04578
25	15	12.97013
26	15	12.89491
27	15	12.82013
28	15	12.74579
29	15	12.67187
30	15	12.59838
31	15	12.52532
32	15	12.45269
33	15	12.38047
34	15	12.30868
35	15	12.2373
36	15	12.16633
37	15	12.09577
38	15	12.02563
39	15	11.95589
40	15	11.88656
41	15	11.81762
42	15	11.74909
43	15	11.68096
44	15	11.61322
45	15	11.54587
46	15	11.47891
47	15	11.41235
48	15	11.34616
49	15	11.28036
50	15	11.21495
51	15	11.14991
52	15	11.08525
53	15	11.02096
54	15	10.95705
55	15	10.89351
56	15	10.83034
57	15	10.76753
58	15	10.70509
59	15	10.64301
60	15	10.58129
		757.5371

Q1 (b): When the size of monthly payment rises, so does the price of the annuity, check below example, now for 60 payments (@ 7% annually), for $25 monthly payment, the price will be $1263.

1	25	24.85502
2	25	24.71088
3	25	24.56758
4	25	24.42511
5	25	24.28346
6	25	24.14264
7	25	24.00263
8	25	23.86344
9	25	23.72505
10	25	23.58746
11	25	23.45067
12	25	23.31468
13	25	23.17947
14	25	23.04505
15	25	22.91141
16	25	22.77854
17	25	22.64645
18	25	22.51511
19	25	22.38455
20	25	22.25473
21	25	22.12567
22	25	21.99736
23	25	21.8698
24	25	21.74297
25	25	21.61688
26	25	21.49152
27	25	21.36689
28	25	21.24298
29	25	21.11978
30	25	20.99731
31	25	20.87554
32	25	20.75448
33	25	20.63412
34	25	20.51446
35	25	20.39549
36	25	20.27722
37	25	20.15962
38	25	20.04272
39	25	19.92648
40	25	19.81093
41	25	19.69604
42	25	19.58182
43	25	19.46826
44	25	19.35536
45	25	19.24312
46	25	19.13152
47	25	19.02058
48	25	18.91027
49	25	18.80061
50	25	18.69158
51	25	18.58318
52	25	18.47542
53	25	18.36827
54	25	18.26175
55	25	18.15585
56	25	18.05056
57	25	17.94588
58	25	17.84181
59	25	17.73834
60	25	17.63548
		1262.562

Q1(c): As health improves, so does life expectancy, and with increased life expectancy, monthly payments will increase too. Let's look at the example below where instead of 60 monthly payments now you expect 80 monthly payments, then price will come to $1595 (for $25 monthly payments).