Question

As per The Economist (June 24, 2017), the Argentinian
government issued its first 100‐year bond, with cash flows denominated in dollars. The bond thus now matures in,
for simplification purposes, 97 years. The current bond has a $1,000 face value and the following monthly, end‐ofmonth
coupon payments: $10/ month for 47 years, $30/month for 20 years, and then $50/month for 30 years. As
Argentina has defaulted on its bonds six times in the past 100 years, you decide that a 18%/year required return is an
appropriate (geometric) average required return over the entire horizon. Thus, use a required return of 18%/year
and answer the following questions.
You might recognize that this bond’s series of cash flows consists of three annuities and a single face‐value cash flow
at maturity. I will refer to the annuities, in chronological order, as Annuity A, Annuity B, and Annuity C. Importantly, I
do not want you to do any calculations here. Rather, I am asking questions about the right approach to ultimately
valuing this annuity.
(a1) The equations for present value of an ordinary annuity are [in math] C / r ∙ ( 1 – 1/(1+r)N ) and [in Excel] –PV(rate,
nper,pmt,,0). State the values that you would use for C (pmt), r (rate), and N (nper) for Annuity A. (a2) State the values
that you would use in the present‐value equation for C (pmt), r (rate), and N (nper) for Annuity B. You do not
need to calculate this present value; just call the answer X (or ⌂ or !!! or gazillion). (a3) State the values that you
would use in the present‐value equation for C (pmt), r (rate), and N (nper) for Annuity C. You do not need to calculate
this present value; just call the answer Z (or ⌂ or !!! or gazillion). (b1) Write the simple math equation for transforming
X (from part a2) into a value today. (b2) Write the simple math equation for transforming Z (from part a3)
into a value today. (b3) Write the simple math equation for transforming the $1,000 face‐value payment into a value
today. [Suggestion: A timeline might be very helpful as you organize your work.]

Answer 1

Annuity A:

N= 47

rate(r) =18%

pmt= 10

FV = 0

calculate for PV, it will be 55.5323

Annuity B

N= 20

rate(r) =18%

pmt= 30

FV = 0

calculate for PV, it will be 160.5824

But as we are discounting it to only 20 years it will be at 47th year.

Hence to get the present value we need to discount it by 1.18^47.

final PV = 160.5824/1.18^47= 0.0667

Annuity C

N= 30

rate(r) =18%

pmt= 50

FV = 1000

calculate for PV, it will be 282.8152

But as we are discounting it to only 30 years it will be at the 67th year.

Hence to get the present value we need to discount it by 1.18^67.

final PV = 282.8152/1.18^67= 0.00431

PV of the bond =  55.5323 + 0.0667 + 0.00431 =55.60381

Additionally, I have attached one timeline so that students can check why annuity b and c were discounted by respective years.

Additionally, I have added excel calculation below for more clarity:

0		pv
1	10	8.474576 =(10/1.18^1)
2	10	7.181844 = (10/1.18^2)
3	10	6.086309
4	10	5.157889
5	10	4.371092
6	10	3.704315
7	10	3.13925
8	10	2.660382
9	10	2.254561
10	10	1.910645
11	10	1.61919
12	10	1.372195
13	10	1.162877
14	10	0.985489
15	10	0.83516
16	10	0.707763
17	10	0.599799
18	10	0.508304
19	10	0.430766
20	10	0.365056
21	10	0.30937
22	10	0.262178
23	10	0.222185
24	10	0.188292
25	10	0.159569
26	10	0.135228
27	10	0.1146
28	10	0.097119
29	10	0.082304
30	10	0.069749
31	10	0.05911
32	10	0.050093
33	10	0.042452
34	10	0.035976
35	10	0.030488
36	10	0.025837
37	10	0.021896
38	10	0.018556
39	10	0.015725
40	10	0.013327
41	10	0.011294
42	10	0.009571
43	10	0.008111
44	10	0.006874
45	10	0.005825
46	10	0.004937
47	10	0.004184
48	30	0.010636
49	30	0.009014
50	30	0.007639
51	30	0.006473
52	30	0.005486
53	30	0.004649
54	30	0.00394
55	30	0.003339
56	30	0.00283
57	30	0.002398
58	30	0.002032
59	30	0.001722
60	30	0.001459
61	30	0.001237
62	30	0.001048
63	30	0.000888
64	30	0.000753
65	30	0.000638
66	30	0.000541
67	30	0.000458
68	50	0.000647
69	50	0.000548
70	50	0.000465
71	50	0.000394
72	50	0.000334
73	50	0.000283
74	50	0.00024
75	50	0.000203
76	50	0.000172
77	50	0.000146
78	50	0.000124
79	50	0.000105
80	50	8.88E-05
81	50	7.53E-05
82	50	6.38E-05
83	50	5.4E-05
84	50	4.58E-05
85	50	3.88E-05
86	50	3.29E-05
87	50	2.79E-05
88	50	2.36E-05
89	50	2E-05
90	50	1.7E-05
91	50	1.44E-05
92	50	1.22E-05
93	50	1.03E-05
94	50	8.75E-06
95	50	7.42E-06
96	50	6.28E-06
97	1050	0.000112
		55.60381	PV of BOND