16.3. HOW TO WEIGH YOUR BORROWING ALTERNATIVES 625
Table 16.4:Appalachian Barracuda Corp’s Analysis of Funding Offers- The competing Offers
(a) (b) (b)–(a) 7-year annuity factors
swap rate loan rate spread upfront fee at swap rate atIRR
usd 4.50% 4.00% 0.50% 2.00% 6.002 054 67 5.819 282 33
eur 4.35% 3.80% 0.55% 1.75% 6.046 667 84 5.860 778 76
spot rateusd/eur1.25- Comparing the loans via swap-rate-basedpvs
USDloan:
risk spreads (PV) 200 m× 0. 005 ×︷a(7yrs, swap$)︸︸ ︷
6 .00205467 = usd 6,002,055
upfront 200 m× 0 .02 = 4,000,000
total cost usd 10.002,055
EURloan:
risk spreads (PV) 160 m× 0. 0055 ×a(7yrs, swape)
︷ ︸︸ ︷
6 .046667843 = eur 5.321,068
upfront 160 m× 0 .0175 = 2,800,000
total cost eur 8.121,068
id. inusd: 8.121,068×1.25 = usd 10.151,335
Extra cost ofEUR= usd10.151,335 –10.002,055 = usd 0.149m- Comparing the loans viaIRR-basedpvs
USDloan:YIELD(some start date︷ ︸︸ ︷
”1/ 1 /2001”,︷ 7 years later︸︸ ︷
”12/ 31 /2007”,coupon︷︸︸︷
0. 045 ,︷︸︸︷Vt
98 ,︷︸︸︷VT
100 ,don’t
ask︷︸︸︷
1 ,1 ) = % 4.844
swap rate % 4.000
all-in spread % 0.844cost inusd: 200m×[0. 00844 × (^5) ︸.819 282 33︷︷ ︸
a(7yrs, IRR$)
] = usd 9.823m
EURloan:
YIELD(”1/1/2001”, ”12/31/2007”, 0.0435, 98.25, 100, 1, 1) = % 4.649
swap rate % 3.800
all-in spread % 0.849
cost ineur: 160m×[0. 00849 ×
a(7yrs, IRRe)
︷ ︸︸ ︷
5 .860 778 76 = eur 7.961m
cost inusd: 1. 25 × 7 .961 = usd 9.951m
Extra cost ofEURloan= 9.951m–9.823m = usd 0.128m
Key Method 1 computes thepv-ed spreads using the swap ratesand then adds the upfront. The
resulting cost difference isusd149K. Method 2 computes an internal rate of return (irr)—I show
the spreadsheet command that does it for you—and finds theirris 0.844% above the swap rate
for the dollar loan, and 0.849% for the euro loan. The cost above the swap rate is thenpv’ed at
theirrs.