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On March 28, 2018, Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some securities for sale to the public. Under the terms of the deal, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2048, but investors would receive nothing until then. Investors paid TMCC $24,099 for each of these securities; so they gave up $24,099 on March 28, 2018, for the promise of a $100,000 payment 30 years later.

In our opening case study, why would the Toyota Motor Credit Corporation (TMCC) be willing to accept such a small amount today ($24,099) in exchange for a promise to repay about 9 times that amount ($10,000) in the future (30 years)?

Respuesta :

truonghanhduyen

Answer:

Because they understand that the present value of $100,000 is same or lower than current $24,099 if discounting rate  ≥  4.86%

Explanation:

To find this discounting rate we solve this equatiation:  

Present value of $100,000 payment 30 years ≤ $24,099

$100,000/(1+rate)^30 ≤ $24,099

↔ (1+rate)^30 ≥ 100,000/24,099

↔ (1+rate)^30 ≥ 4.15

↔ (1+rate) ≥ 4.15^(1/30)

↔ (1+rate) ≥ 1.05

↔ rate ≥ 1.0486 – 1

↔ rate ≥  0.0486

↔ Rate ≥ 4.86 %

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