When using the dividend discount model, care must be taken to avoid using a nomi

Question

When using the dividend discount model, care must be taken to
avoid using a nominal dividend growth rate that exceeds the country's
nominal GDP growth rate. Otherwise the firm is forecast to take over the
country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal
GDP growth is 5% pa forever. The firm's total dividends are currently $1
billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's dividend be as large as
the country's GDP?

Explanation / Answer

Vdiv.(1+gdiv)^T=VGDP.(1+rGDP)^T

1b.(1+0.1)^T=1,000b. (1+0.05)^T

(1+0.11+0.05)^T=1,000

ln((1+0.11+0.05)^T)=ln(1,000)

T.ln(1+0.11+0.05)=ln(1,000)

T=ln(1,000)ln(1+0.11+0.05)=148.4899604 years

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